Part 0 Definitions

8/13/2019 Part 0 Definitions

http://slidepdf.com/reader/full/part-0-definitions 1/25

The Pump Handbook Series 1

apor pressure, cavitation,and NP SH are subjectswidely discussed by engi-neers, pumps users, and

pumping equipment suppliers, butunderstood by too few. To graspthese subjects, a basic explanationis required.

VAPOR PRESSURE

Knowledge of vapor pressureis extremely important whenselecting pumps and their

mechanical seals. Vapor pressureis the pressure absolute at which ali quid, at a given temperature,starts to boil or flash to a gas.Absolutepressure (psia) equals thegauge pressure (psig) plus atmos-pheric pressure.

Let’scompare boiling water atsea level in Rhode Island to boil-ing water at an elevation of 14,110feet on top of Pikes Peak inColorado. Water boils at a lowertemperature at altitude becausetheatmospheric pressure is lower.

Water and water containingdissolved air will boil at differenttemperatures. This is because oneis a liquid and the other is a solu-tion. A solution is a liquid with dis-solved air or other gases. Solutionshave a higher vapor pressure than

their parent liquid and boil at a lowertemperature. While vapor pressurecurves are readily available for liq-uids, they are not f or solutions.Obtaining the correct vapor pressurefor a solution often requires actuallaboratory testing.

CAVITATION

Cavitation can create havoc withpumps and pumping systems in theform of vibration and noise. Bearingfailure, shaft breakage, pitting on the

impeller, and mechanical seal leak-age are some of the problems causedby cavitation.

When a liquid boils in the suc-tion line or suction nozzle of a pump,it is said to be “flashing” or “cavitat-ing” (forming cavities of gas in theliquid). This occurs when the pres-sure acting on the liquid is below thevapor pressure of the liquid. Thedamage occurs when these cavitiesor bubbles pass to a higher pressureregion of the pump, usually just pastthe vane tips at the impeller “eye,”

and then collapse or “implode.”NPSH

Net Positive Suction Head is thedifference between suction pressureand vapor pressure. In pump designand application jargon, NPSHA is the

net positive suctionhead available to thepump, and NPSHR isthe net positive suc-tion head requiredby the pump.

The NPSHAmust be equal to or

greater than theNPSHR for a pumpto run properly. Oneway to determine theNPSH A is to mea-sure thesuction pres-sure at the suctionnozzle, then applythe following formu-la:

NPSHA =PB – VP ±Gr+hv

where PB = barometric pres-sure in feet absolute, VP = vaporpressure of the liquid at maximumpumping temperature in feetabsolute, Gr = gauge reading atthe pump suction, in feet absolute(plus if the reading is above baro-metric pressure, minus if the read-ing is below the barometricpressure), and hv = velocity headin the suction pipe in feetabsolute.

NPSH R can only be deter-mined during pump testing. Todetermine i t, the test engineermust reduce the NPSHA to thepump at a given capacity until thepump cavitates. At this point thevibration levels on the pump andsystem rise, and it sounds li kegravel is being pumped. M orethan one engineer has run for theemergency shut-down switch thefirst time he heard cavitation onthe test floor. It’s during thesetests that onegains a real apprecia-tion for the damage that will occur

if a pump is allowed to cavitatefora prolonged period.

CENTRIFUGAL PUMPING

Centrifugal pumping terminol-ogy can be confusing. The follow-ing section addresses these termsand how they are used:

Head is a term used toexpress pressure in both pumpdesign and system design whenanalyzing static or dynamic condi-tions. This relationship isexpressed as:

head in feet =(pressure in psi x 2.31)specific gravity

Pressure in static systems isreferred to as static head and in adynamic system as dynamichead.

To explain static head, let’sconsider three columns of anydiameter, one filled with water,one with gasoline, and one withsalt water (Figure 1). I f thecolumns are 100 ft tall and you

Nomenclature and DefinitionsBY PAT FLACH

V

FIGURE 1

Static head using various liquids.

43psi 52psi32.5 psi

C E N T R I F U GA L P U M P S

H A N D B O O K

100FEET

STATICHEAD

100FEET

STATICHEAD

100FEET

STATICHEAD

WaterSp. Gr. =1.0

GasolineSp.Gr. =.75

SaltWaterSp.Gr. =1.2



2 The Pump Handbook Series

measure the pressure at the bot-tom of each column, the pres-sures would be 43, 32.5, and 52

psi, respectively. This is becauseof the different specific gravities,or weights, of the three liquids.Remember, we are measuringpounds per square i nch at thebottom of the column, not thetotal weight of the liquid in thecolumn.

The following four terms areused in defining pumping systemsand are illustrated in Figure2.

Total static head is the verti-cal distance between the surfaceof the suction source liquid and

the surface level of the dischargeliquid.

Static discharge head is thevertical distance from the center-line of the suction nozzle up tothe surface level of the dischargeliquid.

Static suction head applieswhen the supply is above thepump. It is the vertical distancefrom the centerline of the suctionnozzle up to the liquid surface of thesuction supply.

Static suction lift applies

when the supply is located belowthe pump. I t is the vertical dis-tance from the centerline of thesuction nozzle down to the surfaceof the suction supply liquid.

Velocity, friction, and pressurehead are used in conjunction withstatic heads to define dynamicheads.

Velocity head is the energy ina liquid as a result of it travelingatsome velocity V. It can be thoughtof as the vertical distance a liquidwould need to fall to gain the samevelocity as a liquid traveling in apipe.

Thisrelationship is expressed as:

hv =V2/2g

where V = velocity of theliquid in feet per second and g =32.2 ft/sec2.

Friction head is the headneeded to overcome resistance toliquid flowing in a system. This

at a pump suction flange, convert-ingit to head and correctingto thepump centerline, then adding thevelocity head at the point of thegauge.

Total dynamic dischargehead is the static discharge head

plus the velocity head at the pumpdischarge flange plus the total fric-tion head in the discharge system.

Thiscan be determined in thefieldby taking the discharge pressurereading, converting it to head, andcorrecting it to the pump center-line, then adding the velocityhead.

Total dynamic suction lift isthe static suction lift minus thevelocity head at the suction flangeplus the total friction head in thesuction line. To calculate total

dynamic suction lift, take suctionpressure at the pump suctionflange, convert it to head and cor-rect it to the pump centerline, thensubtract the velocity head at thepoint of thegauge.

Total dynamic head in asystem is the total dynamic dis-charge head minus the totaldynamic suction head when thesuction supply is above the pump.When the suction supply is belowthe pump, the total dynamic head

resistance can come from pipe fric-tion, valves, and fittings. Values infeet of liquid can be found in theHydraulic Institute Pipe FrictionManual.

Pressure head is the pressure infeet of liquid in a tank or vessel on the

suction or discharge sideof a pump. Itis important to convert this pressureinto feet of liquid when analyzing sys-tems so that all units arethe same. If avacuum existsand thevalue is knownin inches of mercury, the equivalentfeet of liquid can be calculated usingthefollowing formula:

vacuumin feet =in. of Hg x 1.13

specific gravity

When discussing how a pumpperforms in service, we use termsdescribing dynamic head. In other

words, when a pump is running it isdynamic. Pumping systems are alsodynamic when liquid is flowingthrough them, and they must be ana-lyzed as such. To do this, the follow-ing four dynamic terms are used.

Total dynamic suction head isthe static suction head plusthe veloc-ity head at the suction flange minusthe total friction head in the suctionline. Total dynamic suction head iscalculated by taking suction pressure

FIGURE 2

Total static head, static discharge head, static suction head,and static suction lift.

TotalStaticHead

StaticDischarge

Head

StaticSuctionHead

StaticDischargeHead

TotalStaticHead

StaticSuction

Lift



The Pump Handbook Series 3

is the total dynamic discharge headplus thetotal dynamic suction lift.

Centrifugal pumps are dynamic

machines that impart energy to liq-uids. This energy is imparted bychanging the velocity of the liquid asit passes through the impeller. Mostof this velocity energy is then con-verted into pressure energy (totaldynamic head) as the liquid passesthrough thecasing or diffuser.

To predict the approximate totaldynamic head of any centrifugalpump, we must go through two steps.First, thevelocity at the outside diam-eter (o.d.) of theimpeller is calculatedusingthe following formula:

v =(rpm x D)/229where v = velocity at the periph-

ery of the impeller in ft per second, D= o.d. of the impeller in inches, rpm= revolutions per minute of theimpeller, and 229 = a constant.

Second, because the velocityenergy at the o.d. or periphery of theimpeller is approximately equal to thetotal dynamic head developed by thepump, we continue by substituting vfrom above into the following equa-tion:

H =v2/2g

where H = total dynamic headdeveloped in ft, v = velocity at theo.d. of the impeller in ft/sec, and g =32.2 ft/sec2.

A centrifugal pump operating ata given speed and impeller diameterwill raise liquid of any specific gravi-ty or weight to a given height.

Therefore, we always think in termsof feet of liquid rather than pressurewhen analyzing centrifugal pumpsand their systems.■

Patrick M . Flach is t he western

hemisphere T echnical Services M anager

for the Industrial Division of EG&G

Sealol.

Have you had a momentary (or continuing) problem with con-verting gallons per minute to cubic meters per second or liters persecond? Join the crowd. Though the metric or SI system is probablyused as the accepted system, more than English units, it still presentsa problem to a lot of engineers.

Authors are encouraged to use the English system. Followingis alist of the common conversions from English to metric units. This isfar from a complete list. It has been limited to conversions frequentlyfound in solving hydraulic engineering problems as they relate topumping systems.

PUMPING UNITS

FLOW RATE

(U.S.) gallons/min (gpm) x 3.785 =liters/min (L/min)(U.S.) gpm x 0.003785 =cubic meters/min (m3/min)cubic feet/sec (cfs) x 0.028 =cubic meters/sec (m3/s)

HEAD

feet (ft) x 0.3048 =meters (m)pounds/square inch (psi) x 6,895 =Pascals (Pa)

POWER

horsepower (Hp) x 0.746 =kilowatts (kW)

GRAVI TATIONAL CONSTANT (g)

32.2 ft./s2 x 0.3048 =9.81 meters/second2 (m/s2)

SPECIFIC WEIGHT

lb/ft3 x 16.02 =kilogram/cubic meter (kg/m3)VELOCITY (V)

ft/s x 0.3048 =meters/second (m/s)

VELOCITY HEAD

V2/2g (ft) x 0.3048 =meters (m)

SPECIFIC SPEED (Ns)

(gpm–ft) x 0.15 =Ns(m3/min–m)Ns =N(rpm)[(gpm)0.5/(ft)0.75]

J. Robert Kr ebs is President of K rebs Consulti ng Service. He serves on

the Pumpsand SystemsEditorial Advisory Board.

Ba sic Uni ts M ultipl y Engli sh x Fa ctor = M etric

Length Feet x 0.3048 =Meter (m)Mass Pound x 0.454 =Kilogram (Kg)Force Pound x 4.448 =Newton (N)Pressure Pound/Square In. (psi) x 6,895 =Pascal (Pa)

Time Seconds x 1 =Seconds (s)Gallon ( US) Gallon x 0.003785 =Meter Cubed ( m3)Gallon (US) Gallon x 3.785 =Liter (L)

TABLE 1. ENGLISH TO M ETRIC CONVERSION

Pumping Terms



4 The Pump Handbook Series

Centrifugal and Positive Displacement Pumpsin the Operating System

n the many differences that existbetween centrifugal and positivedisplacement pumps, one whichhas caused some confusion is the

manner in which they each operatewithin thesystem.

Positive displacement pumps havea series of working cycles, each of which encloses a certain volume of fluid and moves it mechanicallythrough the pump into the system,

regardless of theback pressure on thepump. While themaximum pressuredeveloped is limited only by themechanical strength of the pump andsystem and by the driving poweravailable, the effect of that pressurecan be controlled by a pressure relief or safety valve.

A major advantage of the posi-tive displacement pump is that itcan deli ver consistent capacitiesbecause the output is solely depen-dent on the basic design of thepump and the speed of its driving

mechanism. This means that, if therequired flow rate is not movingthrough the system, the situationcan always be corrected by chang-ing one or both of these factors.

This is not the case with the cen-trifugal pump, which can onlyreact to the pressure demand of thesystem. If the back pressure on acentrifugal pump changes, so willits capacity.

This can be disruptive for anyprocess dependent on a specifi cflow rate, and it can diminish theoperational stability, hydraulic effi-

ciency and mechanical reliability of the pump.

CENTRIFUGAL PUMP

PERFORMANCE CURVE

The interdependency of the sys-tem and the centrifugal pump can beeasily explained with the use of thepump performance curve and thesystem curve.

A centrifugal pump performancecurve is a well known shape whichshows that the pressure the pump

can develop is reduced as the capacityincreases. Conversely, as the capacitydrops, the pressure it can achieve isgradually increased until it reaches amaximum where no liquid can passthrough the pump. Since this is usuallya relatively low pressure, it is rarelynecessary to install a pressure relief orsafety valve.

When discussing the pressuresdeveloped by a centrifugal pump, we

usethe equivalent linear measurementreferred to as “head,” which allows thepump curve to apply equally to liquidsof different densities.

[Head (in feet)=Pressure (in p.s.i.) x2.31+ Specific Gravity of the liquid]

SYSTEM CURVE

The system curve represents thepressures needed at different flow ratesto move the product through the sys-tem. To simplify a comparison withthe centrifugal pump curve, we againuse the ‘head’ measurement. The sys-

tem head consistsof three factors:• static head, or thevertical eleva-tion through which the liquidmust belifted

• friction head, or the head requiredtoovercomethefriction losses inthepipe, the valves and all the fit-tings and equipment

• velocity head, which is the headrequired toacceleratetheflow of liquid through thepump (Velocityhead is generally quitesmall andoften ignored.)

As the static head does not varysimply because of a change in flowrate, the graph would show a straightline. However, both the frictionhead and thevelocity headwill alwaysvary direct-ly with thecapacity. Thecombinationof all threecreates thesystem curve.

When the pump curve is super-imposed on the system curve, thepoint of intersection represents theconditions (H,Q) at which the pumpwill operate.

Pumping conditions changeONL Y through an alteration ineither the pump curve or the sys-tem curve.

When considering possiblemovements in these curves, itshould be noted that there are onlya few conditions which will causethe pump curve to change its posi-tion and shape:

• wear of theimpeller• change in rotational speed• change in impeller diameter• change in liquid viscositySince these conditions don’t nor-

mally develop quickly, any suddenchange in pumping conditions islikely to be a result of a movementin the system curve, which meanssomething in the system haschanged.

Since there are only three ingre-dients in a system curve, one of which is minimal, it follows thateither the static head or the friction

head must have changed for anymovement to take place in the sys-tem curve.

A change in the statichead is normally a result of a change in tank level. If the pump is emptying atank and discharging at afixed elevation, the statichead against which thepump must operate will begradually increasing as the

IBY ROSS C. MACKAY

Head

Capacity

SystemCurve Friction&

VelocityHead

StaticHead

PumpCurve

SystemCurve

H

OQ


H A N D B O O K



ThePumpHandbookSeries 5

suction tank empties. This will causethe system curve to move upwardsas shown.

An increase in friction head canbe caused by a wide variety of con-ditionssuch as the change in a valvesetting or build-up of solids in astrainer. This will give the system

curvea new slope.

Both sets of events produce thesame result: a reduction of flowthrough the system. I f the flow isredirected to a different location(such as in a tank farm), it meansthat the pump is now operating onan entirely new system which willhavea completely different curve.

Thus, it is clear that regardless of the rated capacity of the centrifugalpump, it will only provide what thesystem requires. It is important tounderstand the conditions underwhich system changes occur, theacceptability of the new operatingpoint on the pump curve, and themanner in which it can bemoved.

When the operating conditions of asystem fitted with a centrifugal pumpchange, it is helpful to consider these

curves, focus on how the system iscontrolling the operation of the pump,and then control the system in theappropriateway.■

Ross C. M ackay i s an independent con-

sultant located in Tottenham, Ontario,

Canada. H e is the author of several papers

on the practical aspects of pump mainte-

nance, and a specialist in helping companies

reduce their pump main tenance costs.



6 ThePumpHandbookSeries

avitation is the formationand collapse of vapor bub-bles in a liquid.

Bubble formationoccurs at a point where the pres-sure is less than the vapor pres-sure, and bubble coll apse orimplosion occurs at a point wherethe pressure is increased to thevapor pressure. Figure 1 showsvapor pressure temperature char-acteristics.

This phenomenon can alsooccur with ship propellers and inother hydraulic systems such asbypass orifices and throttlevalves—situations where anincrease in velocity with resultingdecrease in pressure can reducepressure below the liquid vaporpressure.

CAVITATION EFFECTS

BUBBLE FORM ATION PHASE

Flow is reduced as the liquidis displaced by vapor, and

mechanical imbalance occurs asthe impeller passages are partiallyfilled with lighter vapors. Thisresults in vibration and shaftdeflection, eventually resulting inbearing failures, packing or sealleakage, and shaft breakage. Inmulti-stage pumps this can causeloss of thrust balance and thrustbearing failures.

BUBBLE COLLAPSE PHASE

1. Mechanical damage occurs asthe imploding bubbles removesegments of impeller material.

2. Noise and vibration result fromthe implosion. Noise thatsounds like gravel beingpumped is often the user’s firstwarningof cavitation.

NET POSITIVE SUCTION HEAD

When designing a pumpingsystem and selecting a pump, onemust thoroughly evaluate net posi-tive suction head (NPSH) to pre-vent cavitation. A proper analysis

Cavitation and NPSH in Centrifugal PumpsBY PAUL T. LAHR

C

FIGURE 1

Vapor pressures of various liquids related to temperature.

involves both the net positive suctionheads avail able in the system(NPSHA) and the net positive suctionhead required by the pump (NPSHR).

NPSHA is the measurement orcalculation of the absolute pressureabove the vapor pressure at thepump suction flange. Figure 2 illus-trates methods of calculating NPSHAfor various suction systems. Since

friction in the suction pipe is acommon negative component of NPSHA, the value of NPSHA willalways decrease with flow.

NPSHA must be calculated toa stated reference elevation, suchas the foundation on which thepump is to bemounted.

NPSHR is always referencedto the pump impeller center line.


H A N D B O O K

1000

800

600

500

400

300

200

100

80

60

50

40

30

20

10

8

6

5

4

3

2

1.0

.80

.60

.50

.40

.30

.20

.1060 30 0 30 60 90 120 150 180 210 240

28"

28.5"

29"29.1"29.2"29.3"

29.4"

29.5"

29.6"

29.7"29.72"

10"

15"

20"

22.5"

25"

26"

27"

80

60

50

40

30

20

14

1052 05

985

800

600

500

400

300

200

140

100

-60° to 240°F

TEMPERATURE–F

C A R B O N D I O X I D E

N I T R O U S O X I D E

E T H A N E

M O N O C H L O R O T R I F L U O R O M E T H A N E

H Y D R O G E N S U L F I D E

P R O P Y L E N E

P R O P

A N E

A M M O

N I A

C H L O R I N E

M E T H Y L C

H L O R

I D E

S U L F U R

D I O X

I D E

I S O B U

T A N E

B U T A

N E

E T H Y

L C H L

O R I D E

M E T H

Y L F O R

M A T E

D I E T

H Y L E T H

E R

M E T H

Y L E N

E C H L O

R I D E

D I C H L O

R O E T H Y L E N

E

A C E T

O N E

D I C H

L O R O

E T H Y

L E N E

( C I S )

C H L O

R O F O

R M ( T R I C

H L O R

O M E T

H A N E

)

C A R B O

N T E T

R A C H L O

R I D E T R

I C H L

O R O E T H

U L E N

E

W A T E R

H E A V Y W

A T E R

( S P . G R

. A T 7 0

F = 1 . 1 0 6

G A U G E P R E S S U R E –

L B S

. P E R S Q

. I N

.

V A C U U M –

I N C H E S O F M E

R C U R Y

A B S O L U T E P R E S S U R E –

L B S

. P E R S Q

. I N

.




http://slidepdf.com/reader/full/part-0-definitions 8/258 The Pump Handbook Series

(2–3 feet), users should consult thepump manufacturer and the twoshould agree on a suitable NPSH

margin. In these deliberations, fac-tors such as liquid characteristic,minimum and normal NPSHA,and normal operating flow mustbe considered.

SUCTION SPECIFIC SPEED

The concept of suction specif-ic speed (Ss) must be consideredby the pump designer, pumpapplication engineer, and the sys-tem designer to ensure a cavita-tion-free pump with highreliability and the ability to oper-ate over a wide flow range.

N x Q0.5

Ss =——————(NPSHR)0.75

where N =pump rpm

Q =flow rate in gpm at thebest efficiency point

NPSHR =NPSHR at Q withthe maximum impellerdiameter

The system designer shouldalso calculate the system suction

specific speed by substi-tuting design flow rate andthe system designer’s

NPSHA. The pump speedN is generally determinedby the head or pressurerequired in the system.For a low-maintenancepump system, designersand most user specifica-tions require, or prefer, Ssvalues below 10,000 to12,000. However, as indi-cated above, the pump Ssis dictated to a greatextent by the system con-ditions, design flow, head,and the NPSHA.

Figures 5 and 6 areplots of Ss versus flow ingpm for various NPSHAor NPSHR at 3,500 and1,750 rpm. Similar plotscan be made for other commonpump speeds.

Using curves from Figure 5 andFigure 6 allows the system designerto design the system Ss, i.e., for a sys-tem requiring a 3,500 rpm pumpwith 20 feet of NPSHA, the maxi-mum flow must be limited to 1,000

gpm if the maximum Ss is to bemaintained at 12,000. Variousoptions are available, such asreducing the head to allow 1,750rpm (Figure 7). This would allowflows to 4,000 gpm with 20 feet of NPSHA.

Q1

Q2

100% CAP Q3

Q4

NPSH

3%

N P S H R

T O T A L H E A D

FIGURE 4

Typical results of a four-point net posi-tive suction head required (NPSHR) testbased on a 3% head drop.

1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1

3

2

19

8

7

6

5

4

3

2

1

H S V = 2

3

4

5

6 7

8 9 1 0

H S V = 1 2

1 4 1 6 1 8 2 0

2 8

3 2

3 6 4 0

5 0 5 5

6 0 6 5

H S V = 2 4

H S V =

4 5

Solution for

S=N

for N=3,500 rpm

QHsv

0.75

A plot of suction specific speed (Ss) versus flow in gallons per minute (gpm) for various NPSHA orNPSHR at 3,500 rpm. (Single suction pumps. For double suction use 1/2 capacity). Hsv=NPSHR atBEP with maximum impeller diameter.

Q, Capacity, gpm

S ,

S u c t i o n

s p e c i f i c s p e e d

FIGURE 5


http://slidepdf.com/reader/full/part-0-definitions 9/25The Pump Handbook Series 9

It is important forthe pump user to under-stand how critical thesystem design require-ments are to the selec-tion of a reliable,trouble-free pump.

Matching the systemand pump characteristicsis a must. Frequently,more attention is paid tothe discharge side. Yet itis well known that mostpump performanceproblems are causedby problems on thesuction side.

Figure 7 is a typicalplot of the suction anddischarge systems.

It is important thatpoints A, B, and C be wellestablished and under-stood. A is the normaloperating point. B is themaximum flow for cavi-tation-free operation. C isthe minimum stable flow,which is dictated by thesuction specific speed.

As a general rule, the higherthe suction specific speed, thehigher the minimum stable flowcapacity will be. If a pump isalways operated at its best efficien-cy point, a high value of Ss will notcreate problems. However, if thepump is to be operated at reducedflow, then the Ss value must begiven careful consideration.■

REFERENCES

1. Goulds Pump Manual.

2. Durco Pump EngineeringManual.

3. Hydraulic Institute Test

Standards—1988 CentrifugalPumps 1.6.

Paul T. Lahr is the owner of

Pump Technology, a consulting firm.

H e ser v es o n t h e Pumps andSystems Editorial Advisory Board.

H E A D

N P S H - F E E T

GPMC A B

4

3

2

1

FIGURE 7

1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1

4

3

2

19

8

7

6

5

4

3

2

1

H S V = 1 2

H S V = 1

1 0 9

8

6

3

2

1 4

4

5

7 1 6 1 8 2 0

2 8 3 2 3 6 4 0

5 0

H S V = 2 4

H S V = 4

5

Solution for

S=N

for N=1,750 rpm

QHsv0.75

A plot of suction specific speed (Ss) versusflow in gallonsper minute (gpm) for various NPSHA orNPSHR at 1,750 rpm. (Single suction pumps. For double suction use 1/2 capacity.)HSV=NPSHR atBEP with the maximum impeller diameter.

A typical plot of the suction and dischargesystems. Curve1 = pump head capacityperformance, curve 2 = total system curve,curve3 = suction system curveNPSHA,and curve4 = pump NPSHR.

Q, Capacity, gpm

S ,

S u c t i o n

s p e c i f i c s p e e d

FIGURE 6




f a wide receiver has the rightspeed and good hands, all that’sneeded from the quarterback isto throw the ball accurately,

and the team will probably gaingood yardage, maybe even atouchdown.

Believe it or not, much thesame is trueof a pump and itssuc-tion conditions. If it has the rightspeed and is the right size, allthat’s required from the quarter-back is to deliver the liquid at theright pressure and with an evenlaminar flow into the eye of theimpeller.

If the quarterback’s pass is off target, badly timed, or the ball’sturning end over end in the air,the receiver may not be able tohang on to it, and there’s no gainon the play. When that hap-pens, the quarterbackknows he didn’t throw itproperly and doesn’t blamethe receiver. Unfortunately,that’s where the compari-

son ends. The engineering”quarterbacks” tend toblame the pump even whenits their delivery that’sbad!

Just as there are tech-niques a quarterback mustlearn in order to throwaccurately, there are ruleswhich ensure that a liquidarrives at the impeller eye withthe pressure and flow characteris-ticsneeded for reliable operation.

RULE#1.PROVIDESUFFICIENTNPSH

Without gettingtoo complicat-ed on a subject about which com-plete books have been written,let’s just accept the premise thatevery impeller requires a mini-mum amount of pressure energyin the liquid being supplied inorder to perform without cavita-tion difficulties. This pressureenergy is referred to as NetPositive Suction Head Required.

The NPSH Available is sup-plied from the system. I t is solely

a function of the system design onthe suction side of the pump.Consequently, it is in the control of the system designer.

To avoid cavitation, the NPSHavailable from the system must begreater than the NPSH required bythe pump, and the biggest mistakethat can bemadeby a system design-er is to succumb to the temptation toprovide only the minimum requiredat the rated design point. This leavesno margin for error on the part of thedesigner, or the pump, or the system.Giving in to this temptation hasproved to be a costly mistake onmany occasions.

In the simple system as shownin Figure 1, the NPSH Available canbecalculated as follows:

NPSHA =Ha +Hs - Hvp - Hf

whereHa= the head on the surface of the

liquid in the tank. In an open

system like this, it will beatmospheric pressure.

Hs= the vertical distance of thefree surface of the li quidabove the center line of thepump impeller. If the liquid isbelow the pump, thisbecomesa negative value.

Hvp= the vapor pressure of the liq-uid at the pumping tempera-ture, expressed in feet of head.

Hf = the friction losses in thesuction piping.

The NPSH Available may alsobedetermined with this equation:

NPSHA=Ha +Hg +V2/2g - Hvp

where

Ha= atmospheric pressure infeet of head.

Hg= the gauge pressure at thesuction flange in feet of head.

V2= The velocity head at thepoint of measurement of Hg. (Gauge readings do notincludevelocity head.)

RULE#2.

REDUCE THE FRICTIONLOSSES

When a pump is taking itssuction from a tank, it should belocated as close to the tank as pos-sible in order to reduce the effectof friction losses on the NPSH

Available. Yet the pump must befar enough away from the tank toensure that correct piping practicecan be followed. Pipe friction canusually bereduced by using a larg-er diameter line to limit the linearvelocity to a level appropriate tothe particular liquid beingpumped. M any industries workwith a maximum velocity of about5ft./sec., but this is not alwaysacceptable.

RULE#3.

NOELBOWSONTHE

SUCTIONFLANGE

M uch discussion has takenplace over the acceptable configu-ration of an elbow on the suctionflange of a pump. Let’s simplify it.

There isn’t one! There is always an uneven

flow in an elbow, and when one isinstalled on the suction of anypump, it introduces that unevenflow into the eye of the impeller.

This can create turbulence and air

PumpSuctionConditions

BY ROSSC. MACKAY

I

FIGURE1

2g

CENTRIFUGAL PUMP S

HANDBOOK

Ha

Hvp

Hf

Hs




entrainment, which may result inimpeller damage and vibration.

When the elbow is installed

in a horizontal plane on the inletof a double suction pump,uneven flows are introduced intothe opposing eyes of theimpeller, upsetting the hydraulicbalance of the rotating element.Under these conditions the over-loaded bearing will fail prema-turely and regularly if the pumpis packed. If the pump is fittedwi th mechanical seals, the sealwill usually fail instead of thebearing-but just as regularly andoften more frequently.

The only thing worse thanone elbow on the suction of apump is two elbows on the suc-tion of a pump— particularly if they are positioned in planes atright angles to each other. Thiscreates a spinning effect in theliquid which is carried into theimpeller and causes turbulence,inefficiency and vibration.

A well established and effec-tive method of ensuring a lami-nar flow to the eye of theimpeller is to provide the suctionof the pump with a straight run

of pipe in a lengthequivalent to 5-10times the diameter

of that pipe. Thesmall er multipli erwould be used onthe larger pipediameters and viceversa.

RULE#4. STOP AIROR VAPOR ENTERING THE SUCTIONLINE

Any high spotin the suction linecan become filledwith air or vapor which, if trans-ported into the impeller, will createan effect similar to cavitation andwith the same results. Serviceswhich are particularly susceptibleto this situation are those where thepumpage contains a significantamount of entrained air or vapor,as well as those operating on a suc-tion lift, where it can also cause thepump to lose its prime. (Figure3)

A similar effect can becaused by a concentricreducer. The suction of apump should befitted withan eccentric reducer posi-

tioned withthe flat sideuppermost.(Figure4).

If a pumpis taking i tssuction froma sump ortank, the for-mation of vortices candraw air into the suc-tion line. This can usu-ally be prevented byproviding sufficientsubmergence of liquidover the suction open-ing. A bell-mouth designon the opening wi llreduce the amount of submergence required.

Thi s submergence iscompletely independentof the NPSH required bythepump.

It is worthwhilenoting that these vor-

tices are more difficult to trou-bleshoot in a closed tank simplybecause they can’t be seen aseasily.

Great care should be takenin designing a sump to ensurethat any liquid emptying into itdoes so in such a way that airentrained in the inflow does notpass into the suction opening.Any problem of this nature may

require a change in the relativepositions of the inflow and outletif the sump is large enough, orthe use of baffles. (Figure 5)

RULE#5.

CORRECT PIPINGALIGNMENTPiping flanges must be accu-

rately aligned before the boltsare tightened and all piping,valves and associated fittingsshould be independently sup-ported, so as to place no strainon the pump. Stress imposed onthe pump casing by the pipingreduces the probability of satis-factory performance.

FIGURE2

FIGURE4

FIGURE3

Air Pocket

Suction




Under certain conditions thepump manufacturer may identifysome maximum levels of forcesand moments which may beacceptable on the pump flanges.

In high temperature appli ca-tions, some piping misalignmentis inevitable owing to thermalgrowth during the operating cycle.U nder these conditions, thermalexpansion joints are often intro-duced to avoid transmitting pipingstrains to the pump. However, if the end of the expansion jointclo sest t o t he p ump is n otanchored securely, the object of the exercise is defeated as the pip-ing strains are simply passedthrough to the pump.

RULE#6.WHENRULES1 TO5 HAVE BEEN

IGNORED, FOLLOWRULES 1 TO5.

Piping designis one area wherethe basic princi-ples in-volved areregularly ignored,resul ti ng i nhydraulic instabil-

ities in the impeller which trans-late into additional shaft loading,higher vibration levels and pre-mature failure of the seal or bear-in gs. Because there are many

other reasons why pumps couldvibrate, and why seals and bear-ings fail, the trouble is rarelytraced to incorrect piping.

It has been argued thatbecause many pumps are pipedincorrectly and most of them areoperating quite satisfactorily, pip-ing procedure is not important.Unfortunately, satisfactory opera-tion is a relative term, and whatmay be acceptable in one plantmay beinappropriatein another.

Even when ”satisfactory”

pump operation is obtained, that

doesn’t automatically make aquestionable piping practice cor-rect. It merely makes it lucky.

The suction side of a pump ismuch more i mportant than thepiping on the discharge. If anymistakes are made on the dis-charge side, they can usually becompensated for by increasingthe performance capability fromthe pump. Problems on the suc-tion side, however, can be thesource of ongoing and expensivedifficulties which may never betraced back to that area.

In other words, if yourreceivers aren’t performing well,is it their fault? Or does the quar-terback need more training?■

Ross C. Mackay is an indepen-dent consultant who specializes inadvanced technology training forpump maintenance cost reduction.Healso serves ontheeditorial adviso-ryboardfor Pumps and Systems.

Inflow Inflow

To PumpSuction

To PumpSuction

Baffle

FIGURE5




inimum flow can bedetermined by examin-ing each of the factorsthat affect it. There are

five elements that can be quanti-fied and evaluated:

1. Temperature rise (minimumthermal flow)

2. Minimum stable flow

3. Thrust capacity

4. NPSH requirements5. Recirculation

The highest flow calculatedusing these parameters is consid-ered the minimum flow.

TEMPERATURE RISE

Temperature rise comes fromenergy imparted to the liquidthrough hydraulic and mechanicallosses within the pump. Theselosses are converted to heat,whi ch can be assumed to beentirely absorbed by the liquid

pumped. Based on this assump-tion, temperature rise∆ T in °F isexpressed as:

H 1∆ T =————— x——————

778 xCp η – 1

where

H=total headin feet

Cp =specific heat of the liquid,Btu/lbx°F

η =pump efficiency in decimal

form778ft–lbs =energy to raisethetemperature of one pound of water 1°F

To calculate this, the specificheat and allowable temperaturerisemust beknown.

The specific heat for water is1.0, and other specific heats canbe as l ow as 0.5. The specificheats for a number of liquids canbe found in many chemical and

mechanical handbooks.What is the maximum allowable

temperature rise? Pump manufactur-ers usually limit it to 15°F. H owever,this can be disastrous in certain situa-tions. A comparison of the vapor pres-sure to the lowest expected suctionpressureplusNPSH required (NPSHR)by the pump must bemade. The tem-perature where the vapor pressureequals the suction pressure plus theNPSHR is the maximum allowable

temperature. The differencebetween the allowable temperatureand the temperature at the pumpinlet is the maximum allowabletemperature rise. Knowing ∆ T andCp, the minimum flow can bedetermined by finding the corre-sponding headand efficiency.

When calculating the maxi-mum allowable temperature rise,look at the pump geometry. Forinstance, examine the vertical can

Elements of MinimumFlow

BY TERRY M. WOLD

M

A high-pressure vertical pump. A sterisks (*) denote where low-temperature flu id is exposed to hi gher temperatures. F lashin g andvaporization can occur here. Temperature increases as fl uid trav-els from A towards B.

SUCTION

LowPressureLower

Temperature

DISCHARGE

HighPressureHigher

Temperature

CENTRIFUGAL PUMP S

HANDBOOK

FIGURE1




pump in Figure 1. Although pressureincreases as the fluid is pumpedupward through the stages, consider

the pump inlet. The fluid at the inlet(low pressure, low temperature) isexposed to the temperature of thefluid in the discharge riser in thehead (higher pressure, higher tem-perature). This means that the vaporpressure of the fluid at the pumpinlet must be high enough to accom-modate the total temperature risethrough all the stages. If this condi-tion is discovered during the pumpdesign phase, a thermal barrier canbe designed to reduce the tempera-ture that the inlet fluid is exposed to.

Some books, such as the Pump

Handbook (Ref. 5), contain a typicalchart based on water (Cp = 1.0) thatcan be used with the manufacturer’sperformance curve to determinetemperature rise. If the maximumallowable temperature rise exceedsthe previously determined allowabletemperature rise, a heat shield canbe designed and fitted to the pumpduringthe design stage. This require-ment must be recognized during thedesign stage, because once the pumpis built, options for retrofitting thepump with a heat shield are greatly

reduced.MINIMUM STABLEFLOW

M inimum stable flow can bedefined as the flow corresponding tothe head that equals shutoff head. Inother words, outside the ”droop“ inthe head capacity curve. In general,pumps with a specific speed lessthan 1,000 that are designed for opti-mum efficiency have a droopingcurve. Getting rid of this ”hump“requires an impeller redesign; how-ever, note that there will be a loss of efficiency and an increase in NPSHR.

What’s wrong with a droopinghead/capacity curve? A droopingcurve has corresponding heads fortwo different flows. The pump reactsto the system requirements, andthere are two flows where the pumpcan meet the system requirements.As a result, it ”hunts“ or ”shuttles“between these two flows. This candamage the pump and other equip-ment, but it will happen only undercertain circumstances:

1. The liquid pumpedmust be uninhibitedat both the suction

and discharge ves-sels.

2. One element in thesystem must beableto store and returnenergy, i.e., a watercolumn or trappedgas.

3. Something mustupset the system tomake it start hunt-ing, i.e., startinganother pump inparallel or throttling

a valve.

Note: All of thesemust be present at thesame time to cause thepump to hunt.

M i ni mum f lowbased on the shape of the performance curveis not so much a func-tion of the pump as it isa function of the systemwhere the pump isplaced. A pump in a sys-tem where the above

criteria are presentshould not havea droop-ing curve in the zone of operation.

Becausepumps witha drooping head/capacitycurve have higher effi-ciency and a lower operating cost, itwould seem prudent to investigate theinstallation of a minimumflow bypass.

THRUST LOADING

Axial thrust in a vertical turbinepump increases rapidly as flows arereduced and head increased. Based onthe limitations of the driver bearings,flow must be maintained at a valuewhere thrust developed by the pumpdoes not impair bearing life. Find outwhat your bearing life is and ask thepump manufacturer to give specificthrust valuesbased on actual tests.

If a problem exists that cannot behandled by the driver bearings, con-tact the pump manufacturer. Thereare many designs available today forvertical pumps (both single and mul-

tistage) with integral bearings. Thesebearings can be sized to handle thethrust. Thrust can bebalanced by theuse of balanced and unbalancedstages or adding a balance drum, if necessary. These techniques forthrust balancing are used when highthrust motors are not available. It is

worth noting that balanced stagesincorporate wear rings and balanceholes to achieve lower thrust; there-fore, a slight reduction in pump effi-ciency can be expected, and energycosts becomea factor.

NPSHREQUIREMENTS

How many pumps have beenoversized because of NPSH available(NPSHA)? It seems the easiest solu-tion to an NPSH problem is to go tothe next size pump with a larger suc-

FIGURE2

Recir culation zones are always on the pres-sure side of the vane. A shows dischargerecir culation (the front shroud has been l eftout for clarity). B shows inlet recirculation.




Recirculation is caused by over-sized flow channels that allow liquidto turn around or reverse flow whilepumping is going on (Figure 2 showsrecirculation zones). This reversalcauses a vortex that attaches itself tothe pressure side of the vane. If thereis enough energy available and thevelocities are high enough, damagewill occur. Suction recirculation is

reduced by lowering the peripheralvelocity, which in turn increasesNPSH. To avoid thisit is better to rec-ognize the problem in the designstage and opt for a lower-speedpump, two small er pumps, or anincrease in NPSHA.

Di scharge recirculation iscaused by flow reversal and highvelocities producing damaging vor-tices on the pressure side of thevane at the outlet (Figure 2). Thesolution to this problem lies in the

tion, thereby reducing the inlet loss-es. A couple of factors become entan-gled when this i s done. A largerpump means operating back on thepump curve. Minimum flow must beconsidered. Is the curve stable? Whatabout temperature rise? I f there isalready an NPSH problem, an extrafew degrees of temperature rise willnot help the situation. The thrust and

eye diameter will increase, possiblycausing damaging recirculation.When trying to solve an NPSH prob-lem, don’t take the easiest way out.Look at other options that may solvea long-term problem and reduce oper-ating costs.

RECIRCULATION

Every pump has a point whererecirculation begins. But if this is thecase, why don’t more pumps haveproblems?

10 15 20 25 30 35 40

impeller design. The problem is theresult of a mismatched case andimpeller, too little vane overlap in

the impeller design, or trimming theimpeller below the minimum diame-ter for which it was designed.

Recirculation is one of the mostdifficult problems to understand anddocument. M any studies on thetopic have been done over the years.Mr. Fraser’s paper (Ref. 1) is one of the most useful tools for determin-ing where recirculation begins. I n ithe describes how to calculate theinception of recirculation based onspecific design characteristics of theimpeller and he includes charts thatcan be used with a minimum

amount of information. An exampleof Fraser calculations, which showthe requirements to calculate theinception of suction and dischargerecirculation, is shown in Figure 3.

RECIRCULATIONCALCULATIONS

Figure 3 indicates the user-defined variables and charts requiredto make the Fraser calculations forminimum flow. Information to do thedetailed calculations include:

Q = capacity at thebestefficiency point

H = head at thebest efficiencypointNPSHR = net positive suction head

required at thepump suctionN = pump speedNS = pump specific speedNSS = suction specific speedZ = number of impeller vanesh1 = hub diameter (h1 = 0 for sin-

gle suction pumps)D1 = impeller eye diameterD2 = impeller outside diameterB1 = impeller inlet widthB2 = impeller outlet widthR1 = impeller inlet radius

R2 = impeller outlet radiusF1 = impeller inlet areaF2 = impeller outlet areaβ1 = impeller inlet angleβ2 = impeller outlet angle

The above in formation isobtained from the pump manufactur-er curves or impeller design files. Theimpeller design values are usuallyconsidered proprietary information.

K Ve and K Cm2 can bedeterminedfrom the chartsin Figure3.

FIGURE3

I ncipient recirculation. M ini mum flow is approximately 50% of incipient fl ow, whi le minimum intermittent fl ow is approximately

25% of incipient f low. See text under “R ecir culation Calculations”for details

Cm2

U2

Discharge Angleβ2 I nlet Angleβ1

Ve

U1

.14

.12

.10

.08

.06

.04

10 15 20 25 30.02

.10

.12

.14

.16

.18

.20

.22

.24

.26

.28

.30

.32

R1

R2

D2

D1B1

B2

h1

.08




With all of theabove informa-tion at hand, suction recirculationand the two modes of discharge

recirculation can bedetermined.As previously mentioned,Fraser has some empirical chartsat the end of his paper that can beused to estimate the minimumflow for recirculation. A few of the design factors of the impellerare still required. It is best to dis-cuss recirculation with yourpump manufacturer before pur-chasing a pump, in order toreduce the possibility of problemswith your pump and system afterinstallation and start-up.

SUMMARYMinimum flow can be accu-

rately determined if the elementsdescribed above are reviewed bythe user and the manufacturer.Neither has all the information todetermine a minimum flow that

is economical, efficient, and insuresa trouble-free pump life. It takes acoordinated effort by the user and

the manufacturer to come up withan optimum system for pump selec-tion, design, and installation.

REFERENCES

1. F.H. Fraser. Recirculation in cen-trifugal pumps. Presented at theASM E Winter Annual Meeting(1981).

2. A.R. Budris. Sortingout flow recir-culation problems. MachineDesign(1989).

3. J .J . P augh. H ead-vs-capacitycharacteri stics of centri fugal

pumps. Chemical Engineering(1984).

4. I. Taylor. NPSH still pump appli-cation problem. The Oil and Gas

Journal (1978).

5. I.J. Karassik. Pump Handbook.McGraw-Hill (1986).■

Terry Wold has been the engi-

neering manager for Afton Pumpsfor the last four years. He has beeninvolved in pump design for 25years. M r. Wold graduated fromLamar Tech in 1968 with a bache-lor’s degreein mechanical engineer-ing and is currently a registeredengineer in theStateof Texas.

Thanks to P.J . Patel for hiscomments and assistance in prepar-ing thegraphics.




ne of the greatest sourcesof power waste is the prac-tice of oversizing a pumpby selecting design condi-

tions with excessive margins inboth capacity and total head. It isstrange on occasion to encounter agreat deal of attention being paidto a one-point difference in effi-ciency between two pumps whileat the same time potential powersavings are ignored through an

overly conservative attitude inselecting the required conditionsof service.

POWER CONSUMPTION

After all, we are not primarilyinterested in efficiency; we aremore interested in power con-sumption. Pumps are designed toconvert mechanical energy from adriver into energy within a liquid.

This energy within the liquid isneeded to overcome friction loss-es, static pressure differences andelevation differences at the desired

flow rate. Efficiency is nothing butthe ratio between the hydraulicenergy utilized by the process andthe energy input to the pump dri-ver. And without changing theratio itself, if we find that we areassigning more energy to theprocess than is really necessary,we can reduce this to correspondto the true requirement and there-fore reduce the power consump-tion of the pump.

It is true that some capacitymargin should always be includ-ed, mainly to reduce the wear of internal clearances which will,with time, reduce the effectivepump capacity. How much mar-gin to provide is a fairly complexquestion because the wear thatwil l take place varies with thetype of pump in question, the liq-uid handled, the severity of theservice and a number of othervariables.

A centrifugal pump operatingin a given system will deliver acapacity corresponding to the

Effects of OversizingBY: IGOR J . KARASSIK

O

Pump H -Q curve superimposed on system-headcurve

intersection of itshead-capacity curvewi th the system-head curve, as longas the avail ableNPSH is equal to orexceedstherequiredNP SH (Figure 1).

To change this op-erating point in anexisting installationrequires changingeither the head-capacity curve orthe system-headcurve, or both. Thefirst can be accom-plished by varyingthe speed of thepump (Figure 2), orits impeller dia-meter while thesecond requiresaltering the frictionlosses by throttlinga valvein the pumpdischarge (Figure

3). In the majorityof pump install a-tions, the driver isa constant speedmotor, and chang-ing the system-headcurve i s used tochange the pumpcapacity. Thus, if we have providedtoo much excessmargin in the selec-tion of the pumphead-capacity curve,the pump will haveto operatewith con-siderable throttlingto limit its deliverytothedesiredvalue.

If, on the otherhand, we permitthe pump to oper-ate unthrottled,which is more like-ly, theflow into thesystem will increaseuntil that capacityis reached where

FIGURE1

FIGURE2

V arying pump capacity by varying speed

Varying pump capacity by throttling

FIGURE3

CENTRIFUGAL PUMP S

HANDBOOK

H – Q Cur v eSystem-

Head Curve

Capacity

H e a

d

Head-Capacit y at F ull Speed ( N1)

Head-Capacit y at F ull Speed ( N2 )Head -Cap ac it y at F ul l Sp eed ( N3) H3

H2

H1

System-Head Curve

Friction

LossesStaticPressur eor Head

} H e a

d

Capacity Q3 Q2 Q1max

Head-Capacit y at Const ant Speed H

3 H2 H1

System-

Head Curve

FrictionLossesStaticPressur eor Head

}

Capacity Q3 Q2 Q1max

SystemHead Curveby Throttling Valve

H e a

d




the system-head and head-capaci-ty curves intersect.

EXAMPLE

Let’s use a concrete example,for which the maximum requiredcapacity is 2700 gpm, the statichead is 115 ft and the total frictionlosses, assuming 15-year old pipe,are 60 ft. The total head requiredat 2700 gpm is therefore 175 ft.We can now construct a system-head curve, which is shown oncurve A, Figure 4. If we add amargin of about 10% to therequired capacity and then, as isfrequently done, we add some

If we operate it throttled at therequired capacity of 2700 gpm,operating at the intersection of its

head-capacity curve and curve B,the pump will require 165 bhp. The pump has been selected

with too much margin. We cansafely select a pump with a small-er impeller diameter, say 14 in.,with a head-capacity curve asshown on Figure 4. It will inter-sect curve A at 2820 gpm, givingus about 4% margin in capacity,which is sufficient. To limit theflow to 2700 gpm, we will stillhave to throttle the pump slightlyand our system head curve willbecome curve C. The power con-

sumption at 2700 gpmwill now beonly 145 bhp instead of the 165 bhprequired with our first overly con-servative selection. This is a veryrespectable 12% saving in powerconsumption. Furthermore, weno longer need a 200 hp motor. A150 hp motor will do quite well.

The saving in capital expenditureis another bonus resulting fromcorrect sizing.

Our savings may actually beeven greater. In many cases, thepump may be operated unthrot-

tled, the capacity being permittedto run out to the intersection of thehead-capacity curve and curve A.If this were the case, a pump witha 14-3/4 in. impeller would operateat approximately 3150 gpm andtake 177 bhp. I f a 14 in. impellerwere to be used, the pump wouldoperate at 2820 gpm and take148 bhp. We could besavingmorethan 15% in power consumption.

Tables 1 and 2 tabulate thesesavings.

And our real margin of safetyis actually even greater than I have

indicated. Remember that the fric-tion losses we used to construct thesystem-head curve A were basedon losses thr ough 15-year oldpiping. The losses through newpiping are only 0.613 times thelosses we have assumed. The sys-tem-head curve for new piping isthat indicated as curve D in Figure4. If the pump we had originallyselected (with a 14-3/4 in. impeller)were to operate unthrottled, itwould run at 3600 gpm and take

margin to the total head above thesystem-head curve at this rated flow,we end up by selecting a pump for3000 gpm and 200 ft. total head. The

performance of such a pump, with a14-3/4 in. impeller, is superimposed onthesystem-head curve A in Figure 4.

The pump develops excess headat the maximum required capacity of 2700 gpm, and if we wish to operateat that capacity, this excess head willhave to be throttled. Curve “B” is thesystem-head curve that will have tobecreated by throttling.

If we operate at 3000 gpm, thepump will take 175 bhp, and we willhave to drive it with a 200 hp motor.

Eff ect of oversizing a pump

B

A

D

C

H-Q 1800 R.P.M.

143 / 4"Impeller

η − Q 1 4

3 / 4 " I m p e

l l e r

η − Q

1 4 3 / 4 "

I m p e

l l e r

14"Impeller

η − Q 1 4

" I m p e

l l e r

η − Q 1 4 " I m p e l l e r

Static Head

H-Q 1800 R.P.M.

0 1000 2000 3000 4000Capacity in G.P.M.

240

220

200

180

160

140

200

180

160

140

120

100

80

60

90

80

70

60

50

40

30

20

10

B . H . P .

% E f f i c i e n c y

F e e

t T o

t a l H e a

d

FIGURE4




C l e a r l y ,important energysavings can be

achieved if, at thetime of the selec-tion of the condi-tions of service,r e a s o n a b l erestraints are exer-cised t o av oidi n c o r p o r a t i n gexcessive safetymargins into therated conditions of service.

EXISTINGINSTALLATIONS

But what of existing installationsin which the pumpor pumps haveexcessive margins?Is it too late toachieve these sav-ings? Far from it! Asa matter of fact, it ispossible to establishmore accurately thetrue system-head

curve by running a performance testoncethe pump has been installed and

operated. A reasonable margin canthen be selected and several choicesbecomeavailable to theuser:

1. The existing impeller can be cutdown to meet the more realisticconditions of service.

2. A replacement impeller with thenecessary reduced diameter canbe ordered from the pump man-

ufacturer. The originalimpeller is then stored for fu-ture use if friction losses are

ultimately increased with timeor if greater capacities areever required.

3. In certain cases, there may betwo separate impeller designsavailable for the same pump,one of which is of narrowerwidth than the one originallyfurnished. A replacement nar-row impell er can then beordered from the manufactur-er. Such a narrower impellerwill have its best efficiency ata lower capacity than the nor-

mal width impeller. It may ormay not need to beof a small-er diameter than the originalimpeller, depending on thedegree to whi ch excessivemargin had originally beenprovided. Again, the originalimpeller is put away for possi-ble futureuse.■

I gor J . Karassik is SeniorConsulting Engineer for Ingersoll-Dresser Pump Company. He hasbeen involved with thepump industry

for more than 60 years. M r.Karassik is Contributing Editor -Centrifugal Pumps for Pumps andSystemsMagazine.

187.5 bhp. A pump with only a14 in. impeller would intersect the

system-head curve D at 3230 gpmand take 156.6 bhp, with a savingof 16.5%. As a matter of fact, wecould even use a 13-3/4 in. impel-ler. The head-capacity curvewouldintersect curve D at 3100 gpm, andthe pump would take 147 bhp.Now, the savings over using a14-3/4 in. impeller becomes 21.6%(SeeTable 3).

Throttled to 2700 GPM

Impeller 143/4" 14"Curve “B” “C”BHP 165 145Savings 20hp or 12.1%

TABLE 1. COMPARISONOF PUMPSWITH143/4IN. AND14IN. IMPELLERS, WITHTHE SYSTEM THROTTLED

Unthrottled, on Curve“A”

Impeller 143/4" 14"GPM 3150 2820BHP 177 148Savings 29 hp or 16.4%

TABLE 2. COMPARISONOF PUMPSWITHTHESYSTEM UNTHROTTLED

Impeller 143/4" 14" 133/4"

GPM 3600 3230 3100BHP 187.5 156.5 147Savings 31 hp 40.5 hp

16.5% 21.6%

TABLE 3. EFFECT OF DIFFERENT SIZE IMPELLERS INSYSTEM WITHNEWPIPE ANDRESULTINGSAVINGS NEWPIPE (UNTHROTTLEDOPERATION, CURVE“D”)




hen sizing a pump for anew application or eval-uating the performanceof an existing pump, it is

often necessary to account for theeffect of the pumped fluid’s vis-cosity. We are all aware that thehead-capacity curves presented inpump vendor catalogs are pre-pared using water as the pumpedfluid. These curves are adequatefor use when the actual fluid thatwe are interested in pumping has

a viscosity that is less than orequal to that of water. However,in some cases—certain crude oils,for example—this is not thecase.

Heavy crude oils can haveviscosities high enough to increasethe friction drag on a pump’simpellers significantly. The addi-tional horsepower required toovercome this drag reduces thepump’s efficiency. There are sev-eral analyti cal and empiri calapproaches available to estimatethe magnitude of this effect. Someof these are discussed below.

Before beginning the discus-sion, however, it is vital to empha-size the importance of having anaccurate viscosity number onwhich to base our estimates. Theviscosity of most liquids is strong-ly influenced by temperature. Thisrelationship is most often shownby plotting two points on a semi-logarithmic grid and connectingthem with a straight line. The rela-tionship is of the form:

µ =AeB/T

whereµ =the absolute viscosity of the

fluid

AandB=constants

T =the absolute temperature of thefluid

Plotting this relationshiprequires knowledge of two datapoints, and using them effective-ly requires some judgement as to

the normal operating temperatureas well as the minimum tempera-ture that might be expected duringother off-design conditions such asstart-up.

The effect of pressure on theviscosity of most fluids is small.For mineral oils, for example, anincrease of pressure of 33 bars(≈480 psi ) is equivalent to a tem-

FluidViscosityEffects onCentrifugal Pumps

BY: GUNNARHOLE

W FIGURE1

Reproduced from the H ydraulic I nstitute Standards (Fi gure 71)

CENTRIFUGAL PUMP S

HANDBOOK




perature drop of 1°C. The following definitions are

used when discussing fluids andviscosity. There are five basictypes of liquid that can be differ-entiated on the basis of their vis-cous behavior; they are:

NON-NEWTONIAN

These are fluids where theshear rate-shear stress relationshipis nonlinear. They can be divided

into four categories:• Bingham-plastic fluids are

those in which there is noflow until a threshold shearstress is reached. Beyond thispoint, viscosity decreases withincreasing shear rate. M ostslurries have this property, asdoes America’s favorite veg-etable, catsup.

• Dilatant fluids are those of whi ch vi scosity increaseswi th increasing shear rate.Examples are candy mixtures,

clay slurries, and quicksand.

• Pseudo-plastic fluids are simi-lar to Bingham-plastic fluids,except there is no definiteyield stress. Many emulsionsfall into this category.

• Thixotropic fluids are those of which viscosity decreases to aminimum level as their shearrate increases. Their viscosityat any particular shear ratemay vary, depending on theprevious condition of thefluid.

Examples are asphalt, paint,molasses, and drilling mud.

There are two other termswith which you should befamiliar:

• Dynamic or absolute viscosityis usually measured in termsof centipoiseand has the unitsof forcetime/length2.

• Kinematic viscosity is usuallymeasured in terms of centis-tokes or ssu (Saybolt SecondsUniversal). It is related toabsolute viscosity as follows:

kinematicviscosity=absoluteviscosity/mass density

The normal practice is for thisterm to have the units of length2/time. Note:

1cSt=cP xspgr

1cSt=0.22xssu– (180/ssu)

1cP=1.45E-7lbf – s/in2

1Reyn=1lbf – s/in2

NEWTONIAN

These are fluids where viscosity is

constant and independent of shear

rate, and where the shear rateis linear-

ly proportional to the shear stress.

Examples are water and oil.

FIGURE2

Reproduced from the Hydraulic I nstitute Standards (Fi gure 72 )




The process of determiningthe effect of a fluid’s viscosity onan operating pump has been stud-ied for a number of years. In thebook Centrifugal and A xial FlowPumps, A.J. Stepanoff lists thelosses that affect the performanceof pumps as being of the follow-ing types:

• mechanical losses

• impeller losses

• leakage losses

• disk friction lossesOf all external mechanical

losses, disk friction is by far themost important, according toStepanoff. This is particular-ly true for pumps designed withlow specif ic speeds. Stepanoff gives a brief discussion of thephysics of a rotating impeller andemerges with a simple equationthat summarizes the drag forceacting upon it:

(hp)d =Kn3D5

where

K=arealconstant

n=thepumpoperatingspeed

D=theimpellerdiameter

The explana-tion further de-scribes the motionof f l ui d i n th e

immediate neigh-borhood of thespinning impeller.

There Stepanoff mentions the exper-imental results of others demonstrat-ing that, by reduc-ing the clearancebetween the sta-tionary casing andthe impeller, the re-quired power canbe reduced. Healso writes about

the detail s of some investigationsthat demonstrate the beneficialeffect of good surface fi nishes onboth the stationary and rotating sur-faces. Included is a chart preparedby Pfleiderer, based on work byZumbusch and Schultz-Grunow,that gives friction coefficients forcalculating disk friction losses. Thechart is used in conjunction withthe following equation:

(hp)d=KD2γ u3

where

K =a constant based on the Reynoldsnumber

D=impellerdiameter

γ =fluiddensity

u=impellertipspeed

Like most of Stepanoff’s writing,this presentation contains great depthwith considerable rigor. It makesinteresting reading if you are willingto put forth the time. Those of us

who need a quick answer to a par-ticular problem may need to lookelsewhere for help.

In the book, Centrifugal

Pumps, V. Lobanoff and R. Rossdiscuss the effect of viscous fluidson the performance of centrifugalpumps. They make the point thatbecause the internal flow pas-sages in small pumps are propor-tionally larger than those in largerpumps, the smaller pumps wi llalways be more sensitive to theeffects of viscous fl uids. T heyalso introduce a diagram from thepaper “Engineering and SystemDesign Considerations for PumpSystems and Viscous Service,” byC.E . Petersen, presented atPacifi c Energy Association,October 15, 1982. I n this dia-gram, it is recommended that themaximum fluid viscosity a pumpshould be allowed to handle belimited by the pump’s dischargenozzle size. The relationship isapproximately:

viscositymax =300(Doutletnozzle –1)

where

viscosityis giveninterms ofssu

Dis measuredininchesWith respect to the prediction

of the effects of viscous liquids onthe performance of centrifugalpumps, L obanoff and Ross directthe reader to the clearly definedmethodology of the HydraulicInstitute Standards. This techniqueis based on the use of two nomo-grams on pages 112 and 113 of the14th edition (Figures 71 and 72).

They are reproduced here asFigures 1 and 2. They are intended

WaterCurve-Based

Performance %ofBEP Capacity60% 80% 100% 120%

Capacity, gpm 450 600 750 900Differential Head, ft. 120 115 100 100Efficiency 0.70 0.75 0.81 0.75Horsepower 18 21 21 27Viscous (1,000ssu)PerformanceCapacity, gpm 423 564 705 846Differential Head, ft. 115 108 92 89Efficiency 0.45 0.48 0.52 0.48Horsepower 25 29 28 36

TABLE 1. WATER-BASEDANDVISCOUS PERFORMANCE

Note: Pumpedfluid specific gravity=0.9

Correction

Factor

Dx1 Dx2 Dx3 Dx4 Dx5 Dx6

Cη 1.0522 -3.5120E-02 -9.0394E-04 2.2218E-04 -1.1986E-05 1.9895E-07

CQ 0.9873 9.0190E-03 -1.6233E-03 7.7233E-05 -2.0528E-06 2.1009E-08

CH0.6 1.0103 -4.6061E-03 2.4091E-04 -1.6912E-05 3.2459E-07 -1.6611E-09

CH0.8 1.0167 -8.3641E-03 5.1288E-04 -2.9941E-05 6.1644E-07 -4.0487E-09

CH1.0 1.0045 -2.6640E-03 -6.8292E-04 4.9706E-05 -1.6522E-06 1.9172E-08

CH1.2 1.0175 -7.8654E-03 -5.6018E-04 5.4967E-05 -1.9035E-06 2.1615E-08

TABLE 2. POLYNOMIAL COEFFICIENTS



for use on pumps with BEPsbelow and above 100 gpm, respec-tively, which permits the user toestimate the reduction of head,

capacity, and efficiency that a vis-cous fluid will produce on a pumpcurve originally generated withwater. A variation on this tech-niqueis described below.

The followi ng example istaken from pages 114-116 of theHydraulic Institute Standards sec-tion on centrifugal pump applica-tions. There, the use of Figure 72,“Performance Correction ChartFor Viscous Liquids,” is discussed.

Table 1 was calculated using poly-nomial equations developed toreplace the nomogram presentedin Figure72. The results of the cal-culation are within rounding errorof those presented in the standard.And the approach has the addi-tional benefit of being more conve-nient to use, once it has been setup as a spreadsheet.

In the course of curve-fittingFigure 72, it was convenient todefine a term known as pseudoca-pacity:

pseudocapacity=

1.95(V)0.5[0.04739(H)0.25746(Q)0.5]-0.5

where

V=fluidviscosityincentistokes

H=headriseper stageatBEP, mea-

suredinfeet

Q=capacityatBEP ingpm

Pseudocapacity is used with thefollowing polynomial coefficients todetermine viscosity correction termsthat are very close to those given byFigure 72 in the Hydraulic InstituteStandards. These polynomials havebeen checked throughout the entirerange of Figure 72, and appear to giveanswers within 1.0% of those foundusing thefigure.

The polynomial used is of theform:

Cx =Dx1 +Dx2P +Dx3P

2

+Dx4P

3

+Dx5P4 +Dx6P5

where

Cx is the correctionfactor that must be

appliedtotheterminquestion

Dxn arethepolynomialcoefficients listed

inTable2

P is the pseudocapacity term definedabove

For comparison, the correction

factors for the example above (tabu-lated in Table 7 of the HydraulicInstitute Standards) and those calculat-ed using the polynomial expressionsaboveare listed in Table 3.

The problem of selecting a pumpfor use in a viscous service is relative-ly simple once the correction coeffi-cients have been calculated. If, forexample, we had been looking for apump that could deliver 100 feet of

head at a capacity of 750 gpm, wewould proceed as follows:

Hwater =Hviscous service/CH1.0

Qwater =Qviscous service/CQ

The next step would be tofind a pump having the requiredperformance on water. Af terdetermining the efficiency of thepump on water, we would correctit for the viscous case as shownabove:

ηviscousservice=ηwater xCη

The horsepower required bythe pump at this point would becalculated asfollows:

hpviscous service=

(QviscousservicexHviscousservicexspgr)

(3,960xηviscous service)

As with water service, thehorsepower requirements at off-design conditions should alwaysbe checked. ■

Gunnar Hole is a principal in Trident Engineering, I nc. inHouston, TX. H e has been involvedin the selection, installation, andtroubleshooting of rotating equip-ment for the past 15 years. M r.Hole is a graduate of the Universityof Wisconsin at Madison and is aRegistered Professional Engineer in

Texas.


Cη CQ CH0.6 CH0.8 CH1.0 CH1.2

Per Table7 of HI Standards 0.635 0.95 0.96 0.94 0.92 0.89

Per Polynomial Expressions 0.639 0.939 0.958 0.939 0.916 0.887

TABLE 3. CORRECTIONFACTOR COMPARISON




Presented below is a descriptionof the problem, definitions of some of the more important terms used, andreferences that can beconsulted for amore thorough review. A table alsocompares three of the most commonbalancing criteria used in the pumpindustry.

Perhaps the least controversialcomment that can be made to anexperienced equipment specialist isthat “accurate rotor balancing is criti-cal to reliable operation.” I could addsomespice to the conversation by giv-

ing my opinion on how good is goodenough, but I would rather address

the standards used in the pumpindustry and show how they takedifferent approaches to resolve theproblem of balancing rotors.

I use the term rotor repeated-ly in this discussion. For the pur-pose of thi s article, I includepartially and fully assembledpump shaft/sleeve/impeller as-semblies as well as individualpump components installed onbalancing machine arbors in thisdefinition.

The three major criteria usedwill be referred to as theUnbalanced Force Method (UFM ),the Specified Eccentricity Method(SEM), and the Specified CircularVelocity Method (SCVM ).

In the U FM the allowableunbalance permitted in a rotor isthe amount that will result in adynamic force on the rotor systemequal to some percentage of therotor’s static weight. This allow-able unbalance is therefore relatedto theoperating speed of the rotor.

An example of this method can befound in API Standard 610 6thEdition, where the unbalanceforce contributed to a rotor systemby a rotating unbalance is limitedto 10% of the rotor’s static weight.

The SEM attempts to specifybalance quality by limiting thedistance by which the center of mass of the rotor can be offsetfrom the center of rotation of therotor. This method is used inAGMA Standard 515.02, which is

Unbalanced Specified SpecifiedForce Eccentricity Circular

Method Method VelocityAsperAPI610 Asper Method

6thEdition AGMA510.02 AsperAPI610

7thEdition

ResidualUnbalance

(RUB),in.–oz 56347 W j 16εW j 4 W j

where: N2 N

W j =rotorweightper

balanceplane,Ibf N=rpm

ε=eccentricity,in.

Eccentricity(ε)or

Specific Unbalance

in.–oz/lbm 56347 16ε 4

N2 N

in.–lbm/lbm 3522 ε 0.25

N2 N

whereRUB=εW j seeTable2

UnbalanceForce(UBF),

lbfwhere:

UBF=εMω 2 0.10W j εW jN2 W jN

andM =W j/386lbf–s2/in. 35200 140800ω=2πN/60rad/s

CircularVelocity(CV),

in./s 368 εN 0.26

N 9.54

mm/s 9347 2.66εN 0.665

N

whereCV=εωISOStandard1940 G– 9347 G– 2.66εN G– 0.665

BalanceGrade N

he subject of balancingrotors is one of the funda-mentals of rotating equip-ment engineering. A

number of balancing standardshave been developed over theyears to meet the requirements of pump manufacturers and users,and the idea of balancingis simple.Unfortunately, the definitions andmathematics used in describingbalancing problems can be confus-ing. This article compares thesecriteria so the end user can use

consistent reasoning when makingbalancing decisions.

commonly referenced by flexiblecoupling vendors. I t has theadvantage of being conceptuallysimple. For the gear manufactur-ers who developed this standard,it allowed the use of manufactur-ing process tolerances as balanc-ing tolerances. In Paragraph 3.2.7,API 610 7th Edition suggests thatcouplings meeting AGMA 515.02Class 8 should be used unless oth-erwise specified.

The SCVM is based on con-siderations of mechanical similari-

ty. For geometrically similar rigidrotors running at equal peripheralspeeds, the stresses in the rotorand bearings are the same. Thismethod is described in ISOStandard 1940—Balance Quality of Rigid Rotors. It also forms thebasis of AP I Standard 610 7thEdition’s very stringent 4W/N bal-ancing requirement. Standardsbased on this methodology arebecoming more common.

In Table 1 the three balancingcriteria discussed above are com-pared with respectto their effect on

the various parameters involved inbalancing. The terms used in thetable are defined as follows:

RESIDUALUNBALANCE

This is the amount of unbal-ance present or allowed in therotor. It has the units of mass andlength. It is computed by takingthe product of the rotor mass (perbalance plane) times the distancefrom the rotor’s center of mass toits center of rotation. Note that 1in.–oz is equivalent to 72.1 cm–g.

ECCENTRICITY This is the distance that the

center of mass of the rotor is dis-placed from the rotor’s center of rotation. I t has the unit of length.It can also beconsidered as a mea-sure of specific residual unbal-ance, having the units of length–mass/mass. This term isthe basic criterion of SEM balanc-ing rules (see Table 2). Note that 1in. is equivalent to 25.4 mm.

PumpBalancingCriteriaBY GUNNARHOLE

T

TABLE 1. BALANCINGCRITERIA

CENTRIFUGAL PUMP S

HANDBOOK



FLEXIBLE ROTOR The elastic deflection of flexible

rotors sets up additional centrifugalforces that add to the original unbal-ance forces. Such rotors can be bal-anced in two planes for a single speed

only. At any other speed they willbecome unbalanced. Balancing therotor to allow it to run over a range of speeds involves corrections in threeor more planes. This process is calledmulti-plane balancing.

One important point is that thepump/coupling/driver system mustbe considered as a whole when eval-uating balance quali ty. A simplepump rotor can be balanced to meetAPI 610 7th Edition’s 4W/N criteriain a modern balancing machine with-out too much trouble. An electricmotor rotor may be even easier to

balance due to its simple construc-tion. But the coupling connectingthem can be a completely differentmatter.

The coupling will likely havemore residual unbalance than eitherthe pump or the motor. And everytime you take the coupling apart andput i t back together you take thechance of changing its balance condi-tion. As written, API 610 7th Editionallows a coupling to have a specificresidual unbalance nearly 60 timeshigher than for a 3,600 rpm pump.

This can be a significant problem if you use a relatively heavy coupling.

These balancing methods are pri-marily intended for use on rigidrotors—those operating at speedsunder their first critical speed.Flexible rotors, which operate abovetheir first critical speed, are consider-ably more complicated to balance.

The process of balancing flexiblerotors is discussed in ISO Standard5406–The M echanical Balancing of Flexible Rotors and I SO Standard5343–Criteria for Evaluating FlexibleRotor Unbalance.

The basic concepts of rigid andflexible rotor balancing are the same. The main difference is that with rigidrotor balancing we are only con-cerned with the rigid body modes of vibration. With a flexible rotor, wehave to consider some of the highermodes of vibration as well. In thesecases thedeflection of therotor affectsthe mass distribution along its length.In general, each of the modes has tobebalanced independently.

Note: AGMA 515.02refers to several BalanceQuality Classes. Theyaresummarized asfollows:

EquivalentISOAGMA BalanceQualityGrade

Class ε, µ-in. 1,800 rpm 3,600 rpm8 4,000 19.2 38.39 2,000 9.6 19.2

10 1,000 4.8 9.611 500 2.4 4.812 250 1.2 2.4

UNBALANCEFORCE This is the force that is exert-

ed on a rotor system as a result of the non-symmetrical distributionof mass about the rotor’s center of rotation. The units of this term areforce. This term is the basic criteri-on of UFM balancing rules. Note

that 1 lbf is equivalent to 4.45Newton.

CIRCULARVELOCITY

This is the velocity at whichthe center of mass of the rotorrotates around the center of rota-tion. You can think of it as a tan-gential velocity term. It has theunits of length per unit time. Itforms the basis for balancing rulesbased on the ISO Standard 1940series. I n fact, the BalancingGrades outlined in ISO 1940 arereferenced by their allowable circu-lar velocity in millimeters per sec-ond. The balance quality called forin API 610 7th Edition is betterthan the quality that ISO 1940 rec-ommends for tape recorder drivesand grinding machines. ISO 1940recommends G–6.3 and G–2.5 formost pump components, whereAPI 610 calls for the equivalent of G–0.67. Note that 1 in./s is equiva-lentto 25.4 mm/s.

RIGIDROTOR

A rotor is considered rigidwhen it can be balanced by mak-ing mass corrections in any twoarbitraril y selected balancingplanes. After these corrections aremade, the balance will not signifi-cantly change at any speed up tothe maximum operating speed.With the possible exception of home ceiling fans, I believe thattwo-plane balancing is the mini-mum required for rotating equip-ment components.

Appendix I of A PI 610 7thEdition briefly discusses some of the implications of operating arotor near a critical speed. Theguidelines given there recom-mend separation margins that

specify how far away from a criti-cal speed you can operate a rotor. These margins depend on the sys-tem amplification factors (alsoknown as magnification factors),which are directly related to thedamping available for themodeorresonance in question. The netresult of these recommendationsis to limit the maximum operatingamplification factor to a maxi-mum of about 3.75. The amplifi-cation factor can be thought of asa multiplier applied to the masseccentricity, ε, to account for the

effect of system dynamics.Algebraically, the physics of thesituation can be represented asfollows:

x=Xsin(ω t– Φ)

(ω /ω n)2

X=ε ————————————([1– (ω /ω n)2]2 + (2ζω /ω n)2)0.5

2ζω /ω nΦ =tan–1————————

1– (ω /ω n)2

where

x is thedisplacement ofapoint ontherotor

X is themagnitudeof thevibrationatthatpoint

ε is themass eccentricity

ω is the operating speed or fre-quencyoftherotor

Φ is the phaseangle by which theresponselagstheforce

ζ is the damping factor for themodeof vibrationunder consid-eration

X/ε is theamplificationfactor

ω /ω n is theratio of operating speedto the critical speed under con-sideration

A more detailed discussion onthe topic of damped unbalanceresponse (or whirling of shafts)can be found in any introductoryvibration textbook.■

Gunnar Hole is a principal in Trident Engineering, Inc. in Houston, TX.

TABLE 2. BALANCE QUALITY CLASSES

Date post:	04-Jun-2018
Category:	Documents
Upload:	enas-al-khawaldeh
View:	220 times
Download:	0 times

Part 0 Definitions

Documents