design acueduct system.pdf

10.1 PUMP TYPES AND DEFINITIONS

10.1.1 Pump Standards

Pump types are described or defined by various organizations and their respective publi-cations:

• Hydraulics Institute (HI), American National Standard for Centrifugal Pumps forNomenclature, Definitions, Application and Operation [American National StandardsInstitute (ANSI)/HI 1.1-1.5-1994]

• American Petroleum Institute (API), Centrifugal Pumps for Petroleum, Heavy DutyChemical, and Gas Industry Services, Standard 610, 8th ed., August 1995

• American Society of Mechanical Engineers (ASME), Centrifugal Pumps,Performance Test Code PTC 8.2–1990

In addition, there are several American National Standards Institute (ANSI) andAmerican Water Works Associations (AWWA) standards and specifications pertaining tocentrifugal pumps:

• ANSI/ASME B73.1M-1991, Specification for Horizontal End Suction CentrifugalPumps for Chemical Process.

• ANSI/ASME B73.2M-1991, Specification for Vertical In-Line Centrifugal Pumps forChemical Process.

• ANSI/ASME B73.5M-1995, Specification for Thermoplastic and ThermosetPolymer Material Horizontal End Suction Centrifugal Pumps for ChemicalProcess.

• ANSI/AWWA E 101-88, Standard for Vertical Turbine Pumps—Lineshaft andSubmersible Types.

CHAPTER 10PUMP SYSTEM

HYDRAULIC DESIGN

B. E. BossermanBoyle Engineering Corporation

Newport Beach, CA

10.1

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Source: HYDRAULIC DESIGN HANDBOOK

10.1.2 Pump Definitions and Terminology

Pump definitions and terminology, as given in Hydraulics Institute (HI) 1.1-1.5-1994(Hydraulics Institute, 1994), are as follows:

Definition of a centrifugal pump. A centrifugal pump is a kinetic machine convertingmechanical energy into hydraulic energy through centrifugal activity.

Allowable operating range. This is the flow range at the specified speeds with theimpeller supplied as limited by cavitation, heating, vibration, noise, shaft deflection,fatigue, and other similar criteria. This range to be defined by the manufacturer.

Atmospheric head (hatm). Local atmospheric pressure expressed in ft (m) of liquid.

Capacity. The capacity of a pump is the total volume throughout per unit of time atsuction conditions. It assumes no entrained gases at the stated operating conditions.

Condition points

• Best efficiency point (BEP). The best efficiency point (BEP) is capacity and head atwhich the pump efficiency is a maximum.

• Normal condition point. The normal condition point applies to the point on the ratingcurve at which the pump will normally operate. It may be the same as the rated con-dition point.

• Rated condition point. The rated condition applies to the capacity, head, net positivesuction head, and speed of the pump, as specified by the order.

• Specified condition point. The specified condition point is synonymous with ratedcondition point.

Datum. The pump's datum is a horizontal plane that serves as the reference for headmeasurements taken during test. Vertical pumps are usually tested in an open pit with thesuction flooded. The datum is then the eye of the first–stage impeller (Fig. 10.1).

Optional tests can be performed with the pump mounted in a suction can. Regardlessof the pump's mounting, its datum is maintained at the eye of the first-stage impeller.

Elevation head (Z). The potential energy of the liquid caused by its elevation relativeto a datum level measuring to the center of the pressure gauge or liquid surface.

Friction head. Friction head is the hydraulic energy required to overcome frictionalresistance of a piping system to liquid flow expressed in ft (m) of liquid.

Gauge head (hg). The energy of the liquid due to its pressure as determined by a pres-sure gauge or other pressure measuring device.

Head. Head is the expression of the energy content of the liquid referred to any arbi-trary datum. It is expressed in units of energy per unit weight of liquid. The measuringunit for head is ft (m) of liquid.

High-energy pump. High-energy pump refers to pumps with heads greater than 650 ft(200 m) per stage and requiring more than 300 hp (225 KW) per stage.

Impeller balancing

• Single–plane balancing (also called static balancing). Single–plane balancing refersto correction of residual unbalance to a specified maximum limit by removing or

10.2 Chapter Ten



PUMP SYSTEM HYDRAULIC DESIGN

Pump System Hydraulic Design 10.3

FIGURE 10.1 Terminology for a pump with a positive suction head.

adding weight in one correction plane only. This can be accomplished statically usingbalance rails or by spinning.

• Two–plane balancing (also called dynamic balancing). Two plane–balancing referesto correction of residual unbalance to a specified limit by removing or adding weightin two correction planes. This is accomplished by spinning on appropriate balancingmachines.

Overall efficiency (ηOA). This is the ratio of the energy imparted to the liquid (Pw) bythe pump to the energy supplied to the (Pmot); that is, the ratio of the water horsepower tothe power input to the primary driver expressed in percent.

Power

• Electric motor input power (Pmot). This is the electrical input power to the motor.

Pump input power (Pp). This is the power delivered to the pump shaft at the driver topump coupling. It is also called brake horsepower.

Pump output power (Pw). This is the power imparted to the liquid by the pump. It isalso called water horsepower.

Pw � �Q �

39H60

� s� (U.S. units) (10.1)




Pw � �Q �

36H6

� s� (S.I. units) (10.2)

where

Q � flow in gal/min (U.S.) or m3/hr (SI)

H � head in feet (U.S.) or meters (SI)

S � specific gravity

Pw � power in a horsepower (U.S.) or kilowatt (SI)

Pump efficiency (ηp). This is the ratio of the energy imported to the liquid (Pw) to theenergy delivered to the pump shaft (Pp) expressed in percent.

Pump pressures

• Field test pressure. The maximum static test pressure to be used for leak testing aclosed pumping system in the field if the pumps are not isolated. Generally this istaken as 125 percent if the maximum allowable casing working pressure. In caseswhere mechanical seals are used, this pressure may be limited by the pressure-con-taining capabilities of the seal.

Note: Seesure of the pump to 125 percent of the maximum allowable casing workingpressure on the suction split�case pumps and certain other pump types.

• Maximum allowable casing working pressure. This is the hcase pumps and certainother pump types.

• Maximum allowable casing working pressure. This is the highest pressure at the spec-ified pumping temperature for which the pump casing is designed. This pressure shallbe equal to or greater than the maximum discharge pressure. In the case of somepumps (double suction, vertical turbine, axial split case can pumps, or multistage, forexample), the maximum allowable casing working pressure on the suction side may bedifferent from that on the discharge side.

• Maximum suction pressure. This is the highest section pressure to which the pumpwill be subjected during operation.

• Working pressure (pd). This is the maximum discharge pressure that could occur in thepump, when it is operated at rated speed and suction pressure for the given application.

Shut off. This is the condition of zero flow where no liquid is flowing through thepump, but the pump is primed and running.

Speed. This is the number of revolutions of the shaft is a given unit of time. Speed isexpressed as revolutions per minute.

Suction conditions

• Maximum suction pressure. This is the highest suction pressure to which the pumpwill be subjected during operation.

• Net positive suction head available (NPSHA). Net positive suction head available isthe total suction head of liquid absolute, determined at the first-stage impeller datum,less the absolute vapor pressure of the liquid at a specific capacity:

10.4 Chapter Ten




NPSHA � hsa � hvp (10.3)

where

hsa � total suction head absolute � hatm � hs (10.4)

or NPSHA � hatm � hs � hvp (10.5)

• Net positive suction head required (NPSHR). This is the amount of suction head, overvapor pressure, required to prevent more than 3 percent loss in total head from the firststage of the pump at a specific capacity.

• Static suction lift (Is). Static suction lift is a hydraulic pressure below atmospheric atthe intake port of the pump.

• Submerged suction. A submerged suction exists when the centerline of the pump inletis below the level of the liquid in the supply tank.

• Total discharge head (hd). The total discharge head (hd) is the sum of the dischargegauge head (hgd) plus the velocity head (hvd) at point of gauge attachment plus the ele-vation head (Zd) from the discharge gauge centerline to the pump datum:

• Total head (H). This is the measure of energy increase per unit weight of the liquid,imparted to the liquid by the pump, and is the difference between the total dischargehead and the total suction head.

This is the head normally specified for pumping applications since the complete charac-teristics of a system determine the total head required.

hd � hgd � hvd � Zd (10.6)

• Total suction head (hs), closed suction test. For closed suction installations, the pumpsuction nozzle may be located either above or below grade level.

• Total suction head (hs), open suction. For open suction (wet pit) installations, the firststage impeller of the bowl assembly is submerged in a pit. The total suction head (hs)at datum is the submergence (Zw). If the average velocity head of the flow in the pit issmall enough to be neglected, then:

hs � Zw (10.7)

where

Zw � vertical distance in feet from free water surface to datum.

The total suction head (hs), referred to the eye of the first-stage impeller is the alge-braic sum of the suction gauge head (hvs) plus the velocity head (hvs) at point of gaugeattachment plus the elevation head (Zs) from the suction gauge centerline (or manometerzero) to the pump datum:

hs � hgs � hvs � Zs (10.8)

The suction head (hs) is positive when the suction gauge reading is above atmospher-ic pressure and negative when the reading is below atmospheric pressure by an amountexceeding the sum of the elevation head and the velocity head.

Velocity head (hv). This is the kinetic energy of the liquid at a given cross section.Velocity head is expressed by the following equation:





hv � �2v2

g�(10.9)

where v is obtained by dividing the flow by the cross�sectional area at the point of gaugeconnection.

10.1.3 Types of Centrifugal Pumps

The HI and API standards do not agree on these definitions of types of centrifugal pumps(Figs. 10.2 and 10.3). Essentially, the HI standard divides centrifugal pumps into twotypes (overhung impeller and impeller between bearings), whereas the API standarddivides them into three types (overhung impeller, impeller between bearings, and verti-cally suspended). In the HI standard, the “vertically suspended” type is a subclass of the“overhung impeller” type.

10.6 Chapter Ten

FIGURE 10.2 Kinetic type pumps per ANSI/HI-1.1-1.5-1994.





FIG

UR

E 1

0.3

Pum

p cl

ass

type

iden

tific

atio

n pe

r API

610

.




10.8 Chapter Ten

FIG

UR

E 1

0.4

Typi

cal d

isch

arge

cur

ves.





10.2 PUMP HYDRAULICS

10.2.1 Pump Performance Curves

The head that a centrifugal pump produces over its range of flows follows the shape of adownward facing or concave curve (Fig. 10.4). Some types of impellers produce curvesthat are not smooth or continuously decreasing as the flow increases: that is, there may bedips and valleys in the pump curve.

10.2.2 Pipeline Hydraulics and System Curves

A system curve describes the relationship between the flow in a pipeline and the headloss produced; see Fig. 10.5 for an example. The essential elements of a system curveinclude:

• The static head of the system, as established by the difference in water surface eleva-tions between the reservoir the pump is pumping from and the reservoir the pump ispumping to,

• The friction or head loss in the piping system. Different friction factors representingthe range in age of the pipe from new to old should always be considered.

The system curve is developed by adding the static head to the headlosses that occuras flow increases. Thus, the system curve is a hyperbola with its origin at the value of thestatic head.

The three most commonly used procedures for determining friction in pipelines are thefollowing:

10.2.2.1 Hazen-Williams equation. The Hazen-Williams procedure is represented bythe equation:

V � 1.318C R0.63S0.54 (U.S. units) (10.10a)

where: V� velocity, (ft/s), C� roughness coefficient, R hydraulic radius, (ft), and S �fric-tion head loss per unit length or the slope of the energy grade line (ft/ft).

In SI units, Eq. (10.10a) is

V � 0.849CR0.63S0.54 (10.10b)

where V � velocity (m/s), C � roughness coefficient, R � hydraulic radius, (m) and, S� friction head loss per unit length or the slope of the energy gradeline in meters permeter.

A more convenient form of the Hazen-Williams equation for computing headloss orfriction in a piping system is

HL � �D4.

4

7.8

26� ��

QC

��1.85

(10.11a)




10.10 Chapter Ten

FIGURE 10.5 Typical system head-capacity curves.

where HL�headloss, (ft), L � length of pipe, (ft), D � pipe internal diameter, (ft), Q �flow, (ft3/s), and C� roughness coefficient or friction factor.

In SI units, The Hazen-Williams equation is.

HL � ��10L00�� C15

D12

Q.63��1.85

� �10

D.4

7.8

46

L� ��

QC��1.85

(10.11b)

where HL � head loss, (m), Q � flow, (m3/s), D � pipe diameter, (m), and L � pipelength, (m).

The C coefficient typically has a value of 80 to 150; the higher the value, the smootherthe pipe. C values depend on the type of pipe material, the fluid being conveyed (water orsewage), the lining material, the age of the pipe or lining material, and the pipe diameter.Some ranges of values for C are presented below for differing pipe materials in Table 10.1.

TABLE 10.1 Hazen-Williams Coefficents

Pipe Material C Value for Water C Value for Sewage

PVC 135 –150 130 –145

Steel (with mortar lining) 120–145 120–140

Steel (unlined) 120 to 140 110–130 110–130

Ductile iron (with mortar lining) 100–140 100–130





TABLE 10.1 (Continued)

Pipe Material C Value for Water C Value for Sewage

Asbestos cement 120–140 110–135

Concrete pressure pipe 130–140 120–130

Ductile iron (unlined) 80–120 80–110

AWWA Manual M11, Steel Pipe—A Guide for Design and Installation (AWWA,1989), offers the following relationships between C factors and pipe diameters for waterservice:

C � 140 � 0.17d for new mortar-lined steel pipe (U.S. units) (10.12)

� 140 � 0.0066929d (SI units, d in (mm)

C � 130 � 0.16d (U.S. units) for long-term considerations of lining (10.13)

deterioration, slime buildup, and so on.

� 130 � 0.0062992d (SI units, d in mm),

where

C � roughness coefficient or friction factor (See Table 10.1)

d � pipe diameter, inches or millimeters, as indicated above.

10.2.2.2 Manning’s equation. Manning’s procedure is represented by the equation

V � �1.4

n86� R2/3S1/2 (U.S. units) (10.14)

V � �1n� R2/3S1/2 (SI units),

where V�velocity, (f/s or m/s), n�roughness coefficient, R �Hydraulic radius, (ft or m),and S � friction head loss per unit length or the slope of the energy grade line in feet perfoot or meters per meter.

A more convenient form of the Manning equation for computing head loss or frictionin a pressurized piping system is

HL � �4.66

DL

16

(/3

nQ)2

� (U.S. units) (10.15)

� �10.2

D9L

16

(/3

nQ)2

� (SI units)

where n�roughness coefficient, HL � head loss (ft or m), L � length of pipe (ft or m),D�pipe internal diameter (ft or m), and Q�flow (cu3/s or m3/s).

Values of n are typically in the range of 0.010 – 0.016, with n decreasing withsmoother pipes.




10.2.2.3 Darcy-Weisbach equation. The Darcy-Weisbach procedure is represented bythe equation

HL � f �DL

� �2Vg

2

� (10.16)

where f � friction factor from Moody diagram, g � acceleration due to gravity � 32.2(ft/s) (U.S. units) � 9.81 m/s2 (SI units), HL � head loss (ft or m), L � length of pipe (ftor m), D � pipe internal diameter (ft or m), and V � velocity (ft/s or m/sec).

Sanks et al., (1998) discuss empirical equations for determining f values. A disadvan-tage of using the Darcy-Weisbach equation is that the values for f depend on both rough-ness (E/D) and also on the Reynolds number (Re):

R � �VvD� (10.17)

where R = reynolds number (dimensionless), V = fluid velocity in the pipe (ft/s or m/s), D= pipe inside diameter (ft or m), and v = kinematic viscosity (ft2/s or m2/s)

Values for f as a function of Reynold’s number can be determined by the followingequations:

R less than 2000: f � �6R4� (10.18)

R � 2000–4000: ��1

f�� 2 log10 ��

E3/.D7� � �

R2�.51

f�� (10.19)

R greater than 4000: f �(10.20)

where E/D � roughness, with E � absolute roughness, feet or meters, and D � pipe diam-eter, (ft or m).

Equation 10.19 is the Colebrook-White equation, and Eq. 10.20 is an empirical equa-tion developed by Swamee and Jain, in Sanks et al., (1998). For practical purposes, f val-ues for water works pipelines typically fall in the range of 0.016 to about 0.020.

10.2.2.4 Comparisons of f, C, and n. The Darcy-Weisbach friction factor can be com-pared to the Hazen-Williams C factor by solving both equations for the slope of thehydraulic grade line and equating the two slopes. Rearranging the terms gives, in SI units,

f � ��C11.85�� v0.1

15D34

0.167�� (10.21a)

where v is in m/s and D is in m. In U.S. customary units, the relationship is

f � ��C11.85�� v0.1

15D94

0.167�� (10.21b)

0.25��

�log10��E3/.D7�

� �5R.7

0.

49��2

10.12 Chapter Ten




where v is in fps and D is in feet (Sanks et al., 1998).For pipes flowing full and under pressure, the relationship between C and n is

n � 1.12 �CD

S

0.

0

0

.

3

0

7

4� (10.22a)

in SI units, where D is the inside diameter ID in m. In U.S. customary units, the equationis

n � 1.07 �CD

S

0.

0

0

.

3

0

7

4� (10.22b)

where D is the (ID) in ft.

10.2.3 Hydraulics of Valves

The effect of headlosses caused by valves can be determined by the equation for minorlosses:

hL � K �zVg2

� (10.23)

where hL � minor loss (ft or m), K � minor loss coefficient (dimensionless), V � fluidvelocity (ft/s or m/s), and g � acceleration due to gravity (� 32.2 ft�s /s or 9.81 m�s/s).

Headloss or pressure loss through a valve also is determined by the equation

Q � Cv ��P� (U.S. units) � 0.3807Cv ��P� (S.I. units) (10.24)

where Q � flow through valve (gal/m or m3/s), CV � valve capacity coefficient, and �P� pressure loss through the valve (psi or kPa)

The coefficient CV varies with the position of the valve plug, disc, gate, and so forth.CV indicates the flow that will pass through the valve at a pressure drop of 1 psi. Curvesof CV versus plug or disc position (0–90,with 0 being in the closed position) must beobtained from the valve manufacturer’s catalogs or literature.

CV and K are related by the equation

CV �29.85 ��d2

K�� (U.S. units) (10.25)

where d � valve size, (in).

Thus, by determining the value for CV from the valve manufacturer’s data, a value forK can then be calculated from Eq. (10.25). This K value can then be used in Eq. (10.23)to calculate the valve headloss.

10.2.4 Determination of Pump Operating Points—Single Pump

The system curve is superimposed over the pump curve; (Fig. 10.6). The pump operatingpoints occur at the intersections of the system curves with the pump curves. It should be





observed that the operating point will change with time. As the piping ages and becomesrougher, the system curve will become steeper, and the intersecting point with the pumpcurve will move to the left. Also, as the impeller wears, the pump curve moves downward.Thus, over a period of time, the output capacity of a pump can decrease significantly. SeeFig. 10.7. for a visual depiction of these combined effects.

10.2.5 Pumps Operating in Parallel

To develop a composite pump curve for pumps operating in parallel, add the flows togetherthat the pumps provide at common heads (Fig. 10.8). This can be done with identical pumps(those having the same curve individually) as well as with pumps having different curves.

10.2.6 Variable–Speed Pumps

The pump curve at maximum speed is the same as the one described above. The point ona system-head curve at which a variable�speed pump will operate is similarly determinedby the intersection of the pump curve with the system curve. What are known as the pumpaffinity laws or homologous laws must be used to determine the pump curve at reducedspeeds. These affinity laws are described in detail in Chap 12. For the discussion here, therelevant mathematical relationships are Sanks et al., (1998).

�QQ

1

2� � �

nn

1

2� (10.26)

�HH

1

2� � (�

nn

1

2�)2 (10.27)

�PP

1

2� � (�

nn

1

2�)3 (10.28)

where Q�flow rate, H�head, P�power, n�rotational speed, and subscripts 1 and 2 areonly for corresponding points. Equations (10.26) and (10.27) must be applied simultane-ously to ensure that Point 1 “corresponds” to Point 2. Corresponding points fall on parabo-las through the original. They do not fall on system H-Q curves. These relationships,known collectively as the affinity laws, are used to determine the effect of changes inspeed on the capacity, head, and power of a pump.

The affinity laws for discharge and head are accurate because they are based on actualtests for all types of centrifugal pumps, including axial-flow pumps. The affinity law forpower is not as accurate because efficiency increases with an increase in the size of the pump.

When applying these relationships, remember that they are based on the assumptionthat the efficiency remains the same when transferring from a given point on one pumpcurve to a homologous point on another curve. Because the hydraulic and pressure char-acteristics at the inlet, at the outlet, and through the pump vary with the flow rate, theerrors produced by Eq. (10.28) may be excessive, although errors produced by Eqs.(10.26) and (10.27) are extremely small. See Fig. 10.9 for an illustration of the pumpcurves at different speeds.

Example. Consider a pump operating at a normal maximum speed of 1800 rpm, hav-ing a head-capacity curve as described in Table 10.2. Derive the pump curve for operat-ing speeds of 1000—1600 rpm at 200-rpm increments.

The resulting new values for capacity (Q) and head (H) are shown in Table 10.2. The

10.14 Chapter Ten





FIG

UR

E 1

0.6

Det

erm

inin

g th

e op

erat

ing

poin

t for

a s

ingl

e-sp

eed

pum

p w

ith a

fix

ed v

alue

of

h sta

t




values are derived by taking the Q values for the 1800 rpm speed and multiplying themby the ratio (n1/n2) and by taking the H values for the 1800 rpm speed and multiplyingthem by the ratio (n1/n2)2 .

10.3 CONCEPT OF SPECIFIC SPEED

10.3.1 Introduction: Discharge–Specific Speed

The specific speed of a pump is defined by the equation:

Ns � �nHQ

0

0

.7

.5

5

0

� (10.29)

where Ns = specific speed (unitless), n = pump rotating speed (rpm), Q = pump dischargeflow (gal/mm, m3/s, L/s, m3h) (for double suction pumps, Q is one-half the total pumpflow, and H = total dynamic head (ft or m) (for multistage pumps, H is the head per stage),

The relation between specific speeds for various units of discharge and head is givenin Table 10.3, wherein the numbers in bold type are those customarily used (Sank et al.,1998).

Pumps having the same specific speed are said to be geometrically similar. The spe-cific speed is indicative of the shape and dimensional or design characteristics of the pumpimpeller (HI, 1994). Sanks et al. (1998) also gives a detailed description and discussion ofimpeller types as a function of specific speed. Generally speaking, the various types of

10.16 Chapter Ten

FIGURE 10.7 Effect of impeller wear




Pump System Hydraulic Design 10.17H

ead—

Cap

icity

at V

ario

s Po

ints

Poin

t 1Po

int 2

Poin

t 3Po

int 4

Spee

d(r

pm)

1,80

01,

001,

000

200

1,00

018

02,

000

160

3,00

013

0

103 79 58 40

2,66

7

2,33

3

2,00

0

1,66

7

126 97 71 49

1,77

8

1,55

6

1,33

3

1,11

1

142

109 80 56

889

778

667

556

158

121

89 62

0 0 0 0

0,79

0

0,60

5

0,44

4

0,30

9

0,88

9

0,77

7

0,66

7

0,55

5

1,60

0

1,40

0

1,20

0

1,00

0

Rat

ion 1

/n2

Rat

io(n

1/n 2)

2Q

(gp

m)

H(f

eet)

Q (

gpm

)H

(fee

t)Q

(gp

m)

H(f

eet)

Q (

gpm

)H

(fee

t)

Hea

d—C

apic

ity a

t Var

ios

Poin

tsPo

int 1

Poin

t 2Po

int 3

Poin

t 4Sp

eed

(rpm

)

1,80

01,

001,

000

6063

5512

649

189

40 32 24 18 12

168

147

126

105

39 30 22 15

112 98 84 70

44 33 24 17

56 49 42 33

47 36 27 19

0 0 0 0

0,79

0

0,60

5

0,44

4

0,30

9

0,88

9

0,77

7

0,66

7

0,55

5

1,60

0

1,40

0

1,20

0

1,00

0

Rat

ion 1

/n2

Rat

io(n

1/n 2

)2Q

(gp

m)

H(f

eet)

Q (

gpm

)H

(fee

t)Q

(gp

m)

H(f

eet)

Q (

gpm

)H

(fee

t)




10.18 Chapter Ten

FIG

UR

E 1

0.8

Pum

ps o

pera

ting

in p

aral

lel





FIGURE 10.9 Typical Discharge Curves for a Variable Speed Pump

impeller designs are as follows:Type of Impeller Specific Speed Range (U.S. Units)

Radial-vane 500 –4200

Mixed-flow 4200–9000

Axial-flow 9000–15,000

10.3.2 Suction-Specific Speed

Suction-specific speed is a number similar to the discharge specific and is determined bythe equation

S � �NPnSQH0.5

R

0

0.75� (10.30)

where S � suction-specific speed (unitless) n � pump rotating speed (rpm) Q � pumpdischarge flow as defined for Eq. (10.29).

NPSHR � net positive suction head required, as described in Sec. 10.4

The significance of suction-specific speed is that increased pump speed without prop-er suction head conditions can result in excessive wear on the pump’s components(impeller, shaft, bearings) as a result of excessive cavitation and vibration (HydraulicsInstitute, 1994). That is, for a given type of pump design (with a given specific speed),there is an equivalent maximum speed (n) at which the pump should operate.

Rearranging Eq. (10.30) results in

n � �S � N

QP0.

S50

HA0.75

� (10.31)

Equation (10.31) can be used to determine the approximate maximum allowable pump




speed as a function of net positive suction head available and flow for a given type ofpump (i.e., a given suction-specific speed). Inspection of Eq. (10.31) reveals that, for agiven specific speed, the following pump characteristics will occur:

• The higher the desired capacity (Q), the lower the allowable maximum speed. Thus, aproperly selected high-capacity pump will be physically larger beyond what would beexpected due solely to a desired increased capacity.

• The higher the NPSHA, the higher the allowable pump speed.

10.4 NET POSITIVE SUCTION HEAD

Net positive suction head, or NPSH, actually consists of two concepts:

• the net positive suction available (NPSHA), and

• the net positive suction head required (NPSHR).The definition of NPSHA and NPSHR, as given by the Hydraulics Institute (1994),

were presented in Sec. 10.1.

10.4.1 Net Positive Suction Head Available

Figure 10.1 visually depicts the concept of NPSHA. Since the NPSHA is the head availableat the impeller, friction losses in any suction piping must be subtracted when making thecalculation. Thus, the equation for determining NPSHA becomes

NPSHA � hatm � hs � hvp � hL (10.32)

where:

10.20 Chapter Ten

TABLE 10.3 Equivalent Factors for Converting Values of Specific Speed Expressed in One Setof Units to the Corresponding Values in Another Set of Units

Quantity Expressed in Units of

N (rev/min, (rev/min, (rev/min, (rev/min, (rev/min,Q L/s, m3/s, m3/h, gal/mn, ft3/s,H m) m) m) ft) ft)

1.0 0.0316 1.898 1.633 0.0771

31.62 1 .0 60.0 51.64 2.437

0.527 0.0167 1.0 0.861 0.0406

0.612 0.0194 1.162 1.0 0.0472

12.98 0.410 24.63 21.19 1.0

Source: Sanks, et al 1998 For example, if the specific speed is expressed in metric units (e.g., N � rev/min, Q � m3/s, and H � m),

the corresponding value expressed in U.S. customary units (e.g., N � rev/min, Q � gal/min, and H �feet) is obtained by multiplying the metric value by 51.64.





hatm � atmospheric pressure (ft or m).

hs � static head of water on the suction side of the pump (ft or m) (hs is negative ifthe water surface elevation is below the eye of the impeller).

hvp � vapor pressure of water, which varies with both altitude and temperature (ft orm), and

hL � friction losses in suction piping (ft or m), typically expressed as summation ofvelocity heads (KV2/2g) for the various fittings and pipe lengths in the suctionpiping.

Key points in determining NPSHA are as follows (Sanks et al., 1998):

• the barometric pressure must be corrected for altitude,

• storms can reduce barometric pressure by about 2 percent, and

• the water temperature profoundly affects the vapor pressure.

Because of uncertainties involved in computing NPSHA, it is recommended that theNPSHA be at least 5 ft (1.5 m) greater than the NPSHR or 1.35 times the NPSHR as a factorof safety (Sanks et al., 1998). An example of calculating NPSHA is presented in Section10.5.

10.4.2 Net Positive Suction Head Required by a Pump

Hydraulics Institute (1994) and Sanks et al., (1998) have discussed the concept andimplications of NPSHR in detail. Their discussions are presented or summarized as fol-lows. The NPSHR is determined by tests of geometrically similar pumps operated atconstant speed and discharge but with varying suction heads. The development of cav-itation is assumed to be indicated by a 3 percent drop in the head developed as the suc-tion inlet is throttled, as shown in Fig. 10.10. It is known that the onset of cavitationoccurs well before the 3 percent drop in head (Cavi, 1985). Cavitation can develop sub-stantially before any drop in the head can be detected, and erosion indeed, occurs morerapidly at a 1 percent change in head (with few bubbles) than it does at a 3 percentchange in head (with many bubbles). In fact, erosion can be inhibited in a cavitatingpump by introducing air into the suction pipe to make many bubbles. So, because the 3percent change is the current standard used by most pump manufacturers to define theNPSHR, serious erosion can occur as a result of blindly accepting data from catalogs. Incritical installations where continuous duty is important, the manufacturer should berequired to furnish the NPSHR test results. Typically, NPSHR is plotted as a continuouscurve for a pump (Fig. 10.11). When impeller trim has a significant effect on theNPSHR, several curves are plotted.

The NPSH required to suppress all cavitation is always higher than the NPSHR

shown in a pump manufacturer's curve. The NPSH required to suppress all cavitationat 40 to 60 percent of a pump's flow rate at BEP can be two to five times as is neces-sary to meet guaranteed head and flow capacities at rated flow (Fig. 10.10; Taylor,1987). The HI standard (Hydraulics Institute, 1994) states that even higher ratios ofNPSHA to NPSHR may be required to suppress cavitation: It can take from 2 to 20times the NPSHR to suppress incipient cavitation completely, depending on theimpeller's design and operating capacity.

If the pump operates at low head at a flow rate considerably greater than the capacityat the BEP, Eq. (10.33) is approximately correct:




� � �n(10.33)

where the exponent n varies from 1.25 to 3.0, depending on the design of the impeller. Inmost water and wastewater pumps, n lies between 1.8 and 2.8. The NPSHR at the BEPincreases with the specific speed of the pumps. For high-head pumps, it may be necessaryeither to limit the speed to obtain the adequate NPSH at the operating point or to lowerthe elevation of the pump with respect to the free water surface on the suction side i toincrease the NPSHA.

10.4.3 NPSH Margin or Safety Factor Considerations

Any pump and piping system must be designed such that the net positive suction headavailable (NPSHA) is equal to, or exceeds, the net positive suction head required(NPSHR) by the pump throughout the range of operation. The margin is the amount bywhich NPSHA exceeds NPSHR (Hydraulics Institute, 1994). The amount of marginrequired varies, depending on the pump design, the application, and the materials ofconstruction.

Practical experience over many years has shown that, for the majority of pumpapplications and designs, NPSHR can be used as the lower limit for the NPSH avail-able. However, for high�energy pumps, the NPSHR may not be sufficient. Therefore,the designer should consider an appropriate NPSH margin over NPSHR for high-ener-gy pumps that is sufficient at all flows to protect the pump from damage caused bycavitation.

Q at operating point��

Q at BEPNPSHR at operating point��NPSHR at BEP

10.22 Chapter Ten

FIGURE 10.10 Net positive suction head criteria as determined from pump test results.





FIGURE 10.11 NPSH Required to suppress visible cavitation.

10.4.4 Cavitation

Cavitation begins to develop in a pump as small harmless vapor bubbles, substantiallybefore any degradation in the developed head can be detected (Hydraulics Institute, 1994).This is called the point of incipient cavitation (Cavi, 1985; Hydraulics Institute, 1994).

Studies on high-energy applications show that cavitation damage with the NPSHA

greater than the NPSHR can be substantial. In fact, there are studies on pumps that showthe maximum damage to occur at NPSHA values somewhere between 0 and 1 percent headdrop (or two to three times the NPSHR), especially for high suction pressures as requiredby pumps with high impeller-eye peripheral speeds. There is no universally accepted rela-tionship between the percentage of head drop and the damage caused by cavitation. Thereare too many variables in the specific pump design and materials, properties of the liquidand system. The pump manufacturer should be consulted about NPSH margins for thespecific pump type and its intended service on high-energy, low-NPSHA applications.According to a study of data contributed by pump manufacturers, no correlation exists,between the specific speed, the suction specific speed, or any other simple variable andthe shape of the NPSH curve break-off. The design variables and manufacturing variablesare too great. This means that no standard relationship exists between a 3, 2, 1 or 0 per-cent head drop. The ratio between the NPSH required for a 0 percent head drop and theNPSHR is not a constant, but it generally varies over a range from 1.05 to 2.5. NPSH fora 0, 1, or 2 percent head drop cannot be predicted by calculation, given NPSHR.

A pump cannot be constructed to resist cavitation. Although a wealth of literature isavailable on the resistance of materials to cavitation erosion, no unique material propertyor combination of properties has been found that yields a consistent correlation with cavitation damage rate (Sanks et al., 1998).




10.5 CORRECTED PUMP CURVES

Figures 10.6 and 10.9 depict “uncorrected” pump curves. That is, these curves depict apump H-Q curve, as offered by a pump manufacturer. In an actual pumping station design,a manufacturer's pump must be “corrected” by subtracting the head losses that occur inthe suction and discharge piping that connect the pump to the supply tank and the pipelinesystem. See Table 10.4 associated with Fig. 10.12 in the following sample problem in per-forming these calculations. The example in Table 10.4 uses a horizontal pump. If a verti-cal turbine pump is used, minor losses in the pump column and discharge elbow also mustbe included in the analysis. This same example is worked in U.S. units in Appendix 10.Ato this chapter.

Problem

1. Calculation of minor losses. The principal headloss equation for straight sections ofpipe is:

HL � ��10L00�� C15

D12

Q.63��1.85

(10.11a)

where L � length (m), D � pipe diameter (m), Q � flow (m3/s), C � Hazen-Williamsfriction factor.

10.24 Chapter Ten

TABLE 10.4 Calculate Minor Losses

Item in Pipe Size Friction FactorFig. 10.12 Description mm m K * C+

1 Entrance 300 0.30 1.02 90º elbow 300 0.30 0.303 4.5 m of straight pipe 300 0.30 1404 30º elbow 300 0.30 0.205 2 m of straight pipe 300 0.30 1406 Butterfly valve 300 0.30 0.467 1.2 m of straight pipe 300 0.30 1408 300 mm � 200 mm reducer 200 0.20 0.259 150 mm � 250 mm increaser 250 0.25 0.25

10 1 m of straight pipe 250 0.25 14011 Pump control valve 250 0.25 0.8012 1 m of straight pipe 250 0.25 14013 Butterfly valve 250 0.25 0.4614 0.60 m of straight pipe 250 0.25 14015 90º elbow 250 0.25 0.3016 1.5 m of straight pipe 250 0.25 140

17 Tee connection 250 0.25 0.50

*Typical K values. Different publications present other values.†Reasonable value for mortar-lined steel pipe. Value can range from 130 to 145.





The principal headloss equation for fittings is

HL � �0

0

K �2Vg

2

�

where K � fitting friction coefficient, V � velocity (m/s), g � acceleration due to gravi-ty (m�s/s)

Sum of K values for various pipe sizes:

K300 � 1.96

K200 � 0.25

K250 � 2.31

Sum of C values for various pipe sizes:

FIGURE 10.12 Piping system used in example in Table 10.4.




Pipe lengths for 300-mm pipe: L = 7.7 m

Pipe lengths for 250-mm pipe: L = 4.1 m

Determine the total headloss:

HL � HL 300 mm � HL 250 mm � K300 �V2

3

200

gmm

� � K250 mm �V2

2

250

gmm

� � K200 mm �V2

2

200

gmm

�

HL 300 mm � ��170.070�� 140

1�51

0Q.302.63��1.85

� 3.10 Q1.85

HL 250 mm � ��140.010�� 140

1�51

0Q.252.63��1.85

� 4.00 Q1.85

Convert V 2 /2g terms to Q2 terms:

�2Vg2

� � �21g� ��

QA��2

� �21g� ��A

1��2

Q2 � �21g� ��πD

12/4��2

Q2 � �21g� ��π

12D6

4��2Q2 � �

0.0D8

4

26� Q2

Therefore,

K300 mm �V2

3

200

gmm

� � 1.96 ��0(0.0.3802)64�� Q2 = 19.99 Q2

K200 mm �V2

2

200

gmm

� � 0.25 ��0(0.0.2802)64�� Q2 � 12.90 Q2

K250 � 2.31 ��0(0.0.2852)64�� Q2 � 21.15 Q2

V�2250�

�2g

10.26 Chapter Ten

TABLE 10.5 Convert Pump Curve Head Values to Include Minor Piping Losses

Q H (m)L/s m3/s Uncorrected Corrected

0 0 60 60

63 0.063 55 54.74

126 0.126 49 47.99

189 0.189 40 37.74

252 0.252 27 23.01




Total HL � HL 300 mm � HL 250 mm � K300 mm �V 2

230

g0 mm� � K250 mm �

V 2

225

g0 mm� � K200 mm �

V 2

220

g0 mm�

� 3.10 Q1.85 � 4.00 Q1.85 � 19.99 Q2 � 12.90 Q2 � 21.15 Q2

� 7.10 Q1.85 � 54.04 Q2

2. Modification of pump curve. Using the above equation for HL, a “modified”pump curve can then be developed (see Table 10.5)

The H values as corrected must then be plotted. The operating point of the pump isthe intersection of the corrected H-Q curve with the system curve.

3. Calculation of NPSHA. Using the data developed above for calculating the minorlosses in the piping, it is now possible to calculate the NPSHA for the pump. Only theminor losses pertaining to the suction piping are considered: items 1-8 in Fig. 10.12. Forthis suction piping, we have:

K300 mm � 1.96

K200 mm � 0.25

Sum of the C values: pipe length for 300-mm pipe is L � 7.7 m.

Determine the headloss in the suction piping:

HL � HL 300 mm � K300 � K200

� HL300 mm � 1.96 � 0.25V�

2200�

�2gV�

3200�

�2g

V�2200�

�2gV�

3200�

�2g


Tabla 10.6 Computation of NPSHA:

Condition Flow hs hatm hvp HL at Flow NPSH at Flow(m3/s) (m) (m) (m) (m) (m)

High�static suction head 0 9.0 10.35 0.24 0.00 19.11

0.06 9.0 10.35 0.24 0.12 18.99

0.12 9.0 10.35 0.24 0.53 18.58

0.18 9.0 10.35 0.24 1.20 17.91

0.24 9.0 10.35 0.24 2.12 16.99

0.30 9.0 10.35 0.24 3.29 15.81

Low-static suction head 0 1.0 10.35 0.24 0.00 11.11

0.06 1.0 10.35 0.24 0.12 10.99

0.12 1.0 10.35 0.24 0.53 10.58

0.18 1.0 10.35 0.24 1.20 9.91

0.24 1.0 10.35 0.24 2.12 8.99

0.30 1.0 10.35 0.24 3.29 7.82




� 3.10 Q1.85 � 19.99 Q2 � 12.90 Q2

� 3.10 Q1.85 � 32.89 Q2

For Fig. 10.12, assume that the following data apply:

High-water level � elevation 683 m

Low-water level � elevation 675 m

Pump centerline elevation � 674 m

Therefore:

Maximum static head � 683 � 674 � 9 m

Minimum static head � 675 � 674 � 1 m

Per Eq. (10.32), with computation of NPSHA shown in table 10.5

NPSHA � hatm � hs � hvp � hL

For this example, use

hatm � 10.35 m

hvp � 0.24 m at 15°C

hs = 9 m maximum

hs = 1 m minimum

10.6 HYDRAULIC CONSIDERATIONS IN PUMP SELECTION

10.6.1 Flow Range of Centrifugal Pumps

The flow range over which a centrifugal pump can perform is limited, among other things,by the vibration levels to which it will be subjected. As discussed in API Standard 610(American Petroleum Institute, n.d.), centrifugal pump vibration varies with flow, usuallybeing a minimum in the vicinity of the flow at the BEP and increasing as flow is increasedor decreased. The change in vibration as flow is varied from the BEP depends on thepump's specific speed and other factors. A centrifugal pump's operation flow range can bedivided into two regions. One region is termed the best efficient or preferred operatingregion, over which the pump exhibits low vibration. The other region is termed the allow-able operating range, with its limits defined as those capacities at which the pump’s vibra-tion reaches a higher but still “acceptable” level.

ANSI/HI Standard 1.1–1.5 (Hydraulics Institute, 1994) points out that vibration can becaused by the following typical sources:

1. Hydraulic forces produced between the impeller vanes and volute cutwater or diffuserat vane-passing frequency.

2. Recirculation and radial forces at low flows. This is one reason why there is a definiteminimum capacity of a centrifugal pump. The pump components typically are notdesigned for continuous operation at flows below 60 or 70 percent of the flow thatoccurs at the BEP.

10.28 Chapter Ten




3. Fluid separation at high flows. This is one reason why there is also a definite maximumcapacity of a centrifugal pump. The pump components typically are not designed forcontinuous operation of flows above about 120 to 130 percent of the flow that occursat the BEP.

4. Cavitation due to net positive suction head (NPSH) problems. There is a common mis-conception that if the net positive suction head available (NPSHA) is equal to or greaterthan the net positive suction head required (NPSHR) shown on a pump manufacturer'spump curve, then there will be no cavitation. This is wrong! As discussed in ANSI/HI1.1–1.5-1994 (Hydraulics Institute, 1994 and also discussed by Taylor (1987), it takesa suction head of 2 to 20 times the NPSHR value to eliminate cavitation completely.

5. Flow disturbances in the pump intake due to improper intake design.

6. Air entrainment or aeration of the liquid.

7. Hydraulic resonance in the piping.

8. Solids contained in the liquids, such as sewage impacting in the pump and causingmomentary unbalance, or wedged in the impeller and causing continuous unbalance.

The HI standard then states:

The pump manufacturer should provide for the first item in the pump design and estab-lish limits for low flow. The system designer is responsible for giving due considerationto the remaining items.

The practical applications of the above discussion by observing what can happen in aplot of a pump curve-system head curve as discussed above in Fig. 10.6. If the intersec-tion of the system curve with the pump H-Q curve occurs too far to the left of the BEP(i.e., at less than about 60 percent of flow at the BEP) or too far to the right of the BEP(i.e., at more than about 130 percent of the flow at the BEP), then the pump will eventu-ally fail as a result of hydraulically induced mechanical damage.

10.6.2 Causes and Effects of Centrifugal Pumps Operating OutsideAllowable Flow Ranges

As can be seen in Fig. 10.6, a pump always operates at the point of intersection of the sys-tem curve with the pump H-Q curve. Consequently, if too conservative a friction factor isused in determining the system curve, the pump may actually operate much further to theright of the assumed intersection point so that the pump will operate beyond its allowableoperating range. Similarly, overly conservative assumptions concerning the static head inthe system curve can lead to the pump operating beyond its allowable range. See Fig. 10.13for an illustration of these effects. The following commentary discusses the significance ofthe indicated operating points 1 through 6 and the associated flows Q1 through Q6.

• Q1 is the theoretical flow that would occur, ignoring the effects of the minor head loss-es in the pump suction and discharge piping. See Fig. 10.12 for an example. Q1 isslightly to the right of the most efficient flow, indicated as 100 units.

• Q2 is the actual flow that would occur in this system, with the effects of the pump suc-tion and discharge piping minor losses included in the analysis. Q2 is less than Q1, andQ2 is also to the left of the point of most efficient flow. As shown in Fig. 10.7, as theimpeller wears, this operating point will move even further to the left and the pumpwill become steadily less efficient.





• Q1 and Q2 are the flows that would occur assuming that the system head curve that isdepicted is “reasonable,” that is, not unrealistically conservative. If, in fact, the systemhead curve is flatter (less friction in the system than was assumed), then the operatingpoint will be Q3 (ignoring the effects of minor losses in the pump suction and dischargepiping). If these minor losses are included in the analysis, then the true operating pointis Q4. At Q3, the pump discharge flow in this example is 130 percent of the flow thatoccurs at the BEP. A flow of 130 percent of flow at the BEP is just at edge of, and mayeven exceed, the maximum acceptable flow range for pumps (see discussion in Sec.10.6.1). With most mortar-lined steel or ductile-iron piping systems, concrete pipe, orwith plastic piping, reasonable C values should almost always be in the range of 120145 for water and wastewater pumping systems. Lower C usually would be used onlywhen the pumping facility is connected to existing, old unlined piping that may berougher.

• If the static head assumed was too conservative, then the actual operating points wouldbe Q5 or Q6. Q5 is 150 percent of the flow at the BEP. Q6 is 135 percent of the flow atthe BEP. In both cases, it is most likely that these flows are outside the allowable rangeof the pump. Cavitation, inadequate NPSHA, and excessive hydraulic loads on theimpeller and shaft bearings may likely occur, with resulting poor pump performanceand high maintenance costs.

10.6.3 Summary of Pump Selection

In selecting a pump, the following steps should be taken:

1. Plot the system head curves, using reasonable criteria for both the static head range andthe friction factors in the piping. Consider all feasible hydraulic conditions that willoccur:

a. Variations in static head

b. Variations in pipeline friction factor (C value)

Variations in static head result from variations in the water surface elevations (WSE)in the supply reservoir to the pump and in the reservoir to which the pump is pump-ing. Both minimum and maximum static head conditions should be investigated:

• Maximum static head. Minimum WSE in supply reservoir and maximum WSE indischarge reservoir.

• Minimum static head. Maximum WSE in supply reservoir and minimum WSE indischarge reservoir.

2. Be sure to develop a corrected pump curve or modified pump curve by subtracting theminor losses in the pump suction and discharge piping from the manufacturer's pumpcurve (Table 10.5 and Fig. 10.13). The true operating points will be at the intersectionsof the corrected pump curve with the system curves.

3. Select a pump such that the initial operating point (intersection of the system headcurve with pump curve) occurs to the right of the BEP. As the impeller wears, thepump output flow will decrease (Fig. 10.7), but the pump efficiency will actuallyincrease until the impeller has worn to the level that the operating point is to the leftof the BEP.

For a system having a significant variation in static head, it may be necessary toselect a pump curve such that at high static head conditions the operating point is tothe left of the BEP. However, the operating point for the flows that occur a majorityof the time should be at or to the right of the BEP. Bear in mind that high static head

10.30 Chapter Ten





FIG

UR

E 1

0.13

Det

erm

inin

g th

e op

erat

ing

poin

t for

a s

ingl

e-sp

eed

pum

p.




10.32 Chapter Ten

conditions normally only occur a minority of the time: the supply reservoir must beat its low water level and the discharge reservoir must simultaneously be at its max-imum water level—conditions that usually do not occur very often. Consequently,select a pump that can operate properly at this condition—but also select the pumpthat has a BEP which occurs at the flow that will occur most often. See Fig. 10.14for an example.

4. In multiple�pump operations, check the operating point with each combination ofpumps that may operate. For example, in a two-pump system, one pump operatingalone will produce a flow that is greater than 50 percent of the flow that is producedwith both pumps operating. This situation occurs because of the rising shape of thesystem head curve; see Fig. 10.8. Verify that the pump output flows are within thepump manufacturer's recommended operating range; see Fig. 10.13.

5. Check that NPSHA exceeds the NPSHR for all the hydraulic considerations and oper-ating points determined in Steps 1 and 3.

10.7 APPLICATION OF PUMP HYDRAULIC ANALYSIS

TO DESIGN OF PUMPING STATION COMPONENTS

10.7.1 Pump Hydraulic Selections and Specifications

10.7.1.1 Pump operating ranges Identify the minimum, maximum, and design flows forthe pump based on the hydraulic analyses described above. See Fig. 10.14 as an example.

• The flow at 100 units would be defined as the design point.

• There is a minimum flow of 90 units.

• There is a maximum flow of 115 units.

In multiple–pump operation, the combination of varying static head conditions and thedifferent number of pumps operating in parallel could very likely result in operating pointsas follows (100 units � flow at BEP; see accompaning Table 10.7).

Table 10.7 Pump Operating Ranges

Operating Flow Condition Flow Comments(per Pump)

Minimum 70 Maximum static head condition,all pumps operating

Normal 1 100 Average or most frequent operatingcondition: fewer than all pumps

operating, average static head condition. Might also be the case of all pumps operating, minimum static head condition.

Normal 2 110 Fewer than all pumps operating,minimum static head condition

Maximum 1 115 Maximum static head condition,one pump operating

Maximum 2 125 Minimum static head condition,one pump operating





FIG

UR

E 1

0.14

Det

erm

inin

g th

e op

erat

ing

poin

ts f

or a

sin

gle-

spee

d pu

mp

with

var

iatio

n in

val

ues

of h

stat.




Some observations of the above example are:

• The flow range of an individual pump is about 1.8:1 (125 � 70).• The pump was deliberately selected to have its most efficient operating point

(Q � 100) at the most frequent operating condition, not the most extreme condition. Thiswill result in the minimum power consumption and minimum power cost for the system.

• The pump was selected or specified to operate over all possible conditions, not just oneor two conditions.

In variable�speed pumping applications, the minimum flow can be much lower thanwhat is shown in these examples. It is extremely important that the minimum flow be iden-tified in the pump specification so that the pump manufacturer can design the proper com-bination of impeller type and shaft diameter to avoid cavitation and vibration problems.

10.7.1.2 Specific pump hydraulic operating problems. Specific problems that can occurwhen operating a centrifugal pump beyond its minimum and maximum capacities include(Hydraulics Institute, 1994):

• Minimum flow problems. Temperature buildup, excessive radial thrust, suction recir-culation, discharge recirculation, and insufficient NPSHA.

• Maximum flow problems. Combined torsional and bending stresses or shaft deflectionmay exceed permissible limits; erosion drainage, noise, and cavitation may occurbecause of high fluid velocities.

10.7.2 Piping

Having selected a pump and determined its operating flows and discharge heads or pres-sures, it is then desirable to apply this data in the design of the piping. See Fig. 10.12 fortypical piping associated with a horizontal centrifugal pump.

10.7.2.1 Pump suction and discharge piping installation guidelines. Section 1.4 in theHydraulic Institute (HI) publication ANSI/HI 1.1–1.5 (1994) and Chap. 6 in APIRecommended Practice 686 (1996) provide considerable discussion and many recom-mendations on the layout of piping for centrifugal pumps to help avoid the hydraulic prob-lems discussed above.

10.7.2.2 Fluid velocity. The allowable velocities of the fluid in the pump suction and dis-charge piping are usually in the following ranges:

Suction: 3–9 ft/s (4–6 ft/s most common)

1.0–2.7 m/s (1.2–1.8 m/s most common)

Discharge: 5–15 ft/s (7–10 ft/s most common)

1.5–4.5 m/s (2–3 m/s most common)

Bear in mind that the velocities will vary for a given pump system as the operatingpoint on a pump curve (i.e., intersection of the pump curve with the system curve) variesfor the following reasons:

10.34 Chapter Ten




1. Variation in static heads, as the water surface elevations in both the suction and dis-charge reservoirs vary

2. Long-term variations in pipeline friction factors (Fig. 10.5)

3. Long-term deterioration in impeller (Fig. 10.7)

4. Variation in the number of pumps operating in a multipump system (Fig. 10.8).

A suggested procedure for sizing the suction and discharge piping is as follows:

1. Select an allowable suction pipe fluid velocity of 3–5 ft/s (1.0–1.5 m/s) with all pumpsoperating at the minimum static head condition. As fewer pumps are used, the flowoutput of each individual pump will increase (typically by about 20 to 40 percent withone pump operating compared to all pumps operating) with the resulting fluid veloci-ties in the suction piping also increasing to values above the 3–5 ft/s (1.0–1.5 m/s)nominal criteria;

2. Select an allowable discharge pipe fluid velocity of 5–8 ft/s (1.5–2.4 m/s) also with allpumps operating at the minimum static head condition. As discussed above, as fewerpumps are used, the flow output of each individual pump will increase with the result-ing fluid velocities in the discharge piping also increasing in values above the 5–8 ft/s(1.5–2.4 m/s) nominal criteria.

10.7.2.3 Design of pipe wall thickness (pressure design) Metal pipes are designed forpressure conditions by the equation for hoop tensile strength:

t � �2PSDE�

(10.34)

where

t � wall thickness, in or mm

D � inside diameter, in or mm (although in practice, the outside diameter is oftenconservatively used, partly because the ID is not known initially and because itis the outside diameter (OD) that is the fixed dimension: ID then varies with thewall thickness)

P � design pressure (psi or kPa)

S � allowable design circumferential stress (psi or kPa)

E � longitudinal joint efficiency

The design value for S is typically 50 percent of the material yield strength, for “nor-mal” pressures. For surge or transient pressures in steel piping systems, S is typicallyallowed to rise to 70 percent of the material yield strength (American Water WorksAssociation 1989).

The factor E for the longitudinal joint efficiency is associated with the effectivestrength of the welded joint. The ANSI B31.1 (American Society for MechanicalEngineers, 1995) and B31.3 (American Society for Mechanical Engineers, 1996) codesfor pressure piping recommend the values for E given in Table 10.8





TABLE 10.8 Weld Joint Efficiencies

Type of Longitudinal Joint Weld Joint Efficiency Factor (E)

Arc or gas weld (steel pipe)

Single-butt weld 0.80

Double-butt weld 0.90

Single-or double-butt weld with 100% radiography 1.00

Electric resistance weld (steel pipe) 0.85

Furnace butt weld (steel pipe) 0.60

Most steel water pipelines 0.85

Ductile iron pipe 1.0

The wall thickness for plastic pipes [polyvinyl chloride (PVC), high-density polyeth-ylene (HDPE), and FRP] is usually designed in the United States on what is known as thehydrostatic design basis or HDB:

Pt � �D2–tt� � �

HDF

B� (10.35)

where Pt � total system pressure (operating � surge), t � minimum wall thickness (in),D � average outside diameter (in), HDB � hydrostatic design basis (psi) anh F � factorof safety (2.50–4.00)

10.7.2.4 Design of pipe wall thickness (vacuum conditions). If the hydraulic transientor surge analysis (see Chap. 12) indicates that full or partial vacuum conditions may occur,then the piping must also be designed accordingly. The negative pressure required to col-lapse a circular metal pipe is described by the equation:

∆P � �(1 �

2µE

2)SF� ��De��3

(10.36)

where ∆P = difference between internal and external pipeline pressures (psi or kPa) , E =modulus of elasticity of the pipe material (psi or kPa), µ = Poisson's ratio, SF = safety fac-tor (typically 4.0), e = wall thickness (in or m) anh D = outside diameter (in or m)

Because of factors such as end effects, wall thickness variations, lack of roundness,and other manufacturing tolerances, Eq. (10.3b) for steel pipe is frequently adjusted inpractice to

∆P � �50,0

S0F0,000� ��D

e��3

(10.37)

10.7.2.5 Summary of pipe design criteria. The wall thickness of the pump piping sys-tem is determined by consideration of three criteria:

1. Normal operating pressure [Eq. (10.34)], with S � 50 percent of yield strength

2. Maximum pressure due to surge (static � dynamic � transient rise), using Eq. (10.34)with S � 70 percent of yield strength (in the case of steel pipe)

3. Collapsing pressure, if negative pressures occur due to surge conditions (Eq. 10.36).

10.36 Chapter Ten




10.8 IMPLICATIONS OF HYDRAULIC TRANSIENTS

IN PUMPING STATION DESIGN

Hydraulic transient, or surge, analysis is covered in detail in Chap. 12. Surge or hydraulictransient effects must be considered in pump and piping systems because they can causeor result in (Sanks et al., 1998):

• rupture or deformation of pipe and pump casings,

• pipe collapse,

• vibration,

• excessive pipe or joint displacements, or

• pipe fitting and support deformation or even failure.

The pressures generated due to hydraulics, thus, must be considered in the pipe design,as was discussed in Sec. 10.7, above.

10.8.1 Effect of Surge on Valve Selection

At its worst, surges in a piping can cause swing check valves to slam closed violentlywhen the water column in the pipeline reverses direction and flows backward through thecheck valve at a significant velocity before the valve closes completely. Consequently, inpump and piping systems in which significant surge problems are predicted to occur,check valves or pump control valves are typical means to control the rate of closure of thevalve. Means of controlling this rate of closure include

• Using a valve that closes quickly, before the flow in the piping can reverse and attaina high reverse velocity.

• Providing a dashpot or buffer on the valve to allow the valve clapper or disc to closegently.

• Closing the valve with an external hydraulic actuator so that the reverse flowing watercolumn is gradually brought to a halt. This is frequently done with ball or cone valvesused as pump control valves.

The pressure rating of the valve (both the check valve or pump control valve and theadjacent isolation) should be selected with a pressure rating to accommodate the predict-ed surge pressures in the piping system.

10.8.2 Effect of Surge on Pipe Material Selection

Metal piping systems, such as steel and ductile iron, have much better resistance tosurge than do most plastic pipes (PVC, HDPE, ABS, and FRP). The weakness of plasticpipes with respect to surge pressures is sometimes not adequately appreciated because thewave velocity (a) and, hence, the resulting surge pressures are significantly lower than isthe case with metal piping systems. Since the surge pressures in plastic piping are lowerthan those in metal piping systems, there is sometimes a mistaken belief that the entiresurge problem can then be neglected. However, plastic piping systems inherently offer lessresistance to hydraulic transients than do metal piping systems, even with the lower pres-sures. This is particularly the case with solvent or adhesive welded plastic fittings.





HDPE has better resistance to surge pressures than other plastic piping systems. Inaddition, the joints are fusion butt welded, not solvent welded, which results in a strongerjoint. However, HDPE is still not as resistant to surge effects as a properly designed steelor ductile iron piping system.

REFERENCES

American Petroleum Institute,Centrifugal Pumps for Petroleum, Heavy Duty Chemical, and GasIndustry Services, API Standard 610, 8th ed American Petroleum Institute, Washington, DC.

American Society of Mechanical Engineers (ASME), B31.1, Power Piping, ASME, NewYork, 1995.American Society of Mechanical Engineers (ASME), B31.3, Process Piping, ASME, NewYork, 1996American Water Works Association, Steel Pipe—A Guide for Design and Installation, AWWA M11,

3rd ed., American Water Works Association, Denver, CO 1989.Cavi, D., “NPSHR Data and Tests Need Clarification,” Power Engineering, 89:47–50, 1985.Hydraulics Institute, American National Standard for Centrifugal Pumps for Nomenclature,

Definitions, Applications, and Operation, ANSI/HI 1.1–1.5-1994, Hydraulics Institute,Parsippany, NJ, 1994.

American Petroleum Institute, Recommended Practices for Machinery Installation and InstallationDesign, Practice 686, 1st ed. Washington, DC, 1996.

Sanks, R. L., et al., Pumping Station Design, 2nd ed., Butterworths, 1998.Taylor., “Pump Bypasses Now More Important,” Chemical Engineering, May 11, 1987.

10.38 Chapter Ten




Calculation of minor losses and NPSHA in piping and modification of a pump curve(U.S. units)

Part 1. Calculation of Minor Losses

Principal headloss equations

• For straight sections of pipe: HL � �4D.7

4

2.8

L6� ��

QC��1.85

[Sec Eq. (10.11)]

where L = length in feet, D = pipe diameter (ft), Q = flow (ft3/s) anh C = Hazen-Williams friction fac-tor

• For fittings: HL � �0

0

K �2Vg2

� [Sec Eq. (10.23)]

where K � fitting friction coefficient, V � velocity in (ft/s), anh g � acceleration due to gravity[(ft�s)/s]

Sum of K values for various pipe sizes:

• K12 � 1.96

• K8 � 0.25

• K10 � 2.31

Sum of C values for various pipe sizes:

• Pipe lengths for 12-in pipe: L � 26 ft

• Pipe lengths for 10-in pipe: L � 13 ft.

Determine the total headloss:

HL � HL 12in � HL 10in� K12 �V2

2

g12� � K10 �

V2

2

g10� � K8

HL 12in � �(41.27/21(22)64.

)86� ��1

Q40��1.85

� 0.013139Q1.85

HL 10in � �(41.07/21(21)34.

)86� ��1

Q40��1.85

� 0.015936Q1.85

Convert �V2g

2

� terms to Q2 terms

V�28

�

�2g


APPENDIX 10. APUMP SYSTEM

HYDRAULIC DESIGN




�2Vg

2

� � �21g� ��

QA��2

� �21g� ��A

1��2

Q2

� �21g� ��D

12/4��2

Q2

� �21g� ��

12D6

4��2Q2

� �0.02

D5

4

173� Q2

Therefore,

K12 � 1.96 ��0(.1022/51127)4

3�� Q2

� 0.04933 Q2

V�122�

�2g

10.40 Chapter Ten

Friction FactorItem in Description Pipe Size

Fig. 10.12 (in) K* C+

1 Entrance 12 1.0

2 90º elbow 12 0.30

3 15 ft of straight pipe 12 140

4 30º elbow 12 0.20


6 Butterfly valve 12 0.46


8 12 in � 8 in reducer 8 0.25

9 6 in � 10 in increaser 10 0.25


11 Pump control valve 10 0.80


13 Butterfly valve 10 0.46


15 90º elbow 10 0.30


17 Tee connection 10 0.50

*Typical K values. Different publications present other values.†Reasonable value for mortar-lined steel pipe. Value can range from 130 to 145.




K8 � 0.25 ��0.(082/1521)74

3�� Q2

� 0.031859 Q2

K10 � 2.31 ��0(.1002/51127)4

3�� Q2

� 0.12058 Q2

Total HL � HL 12in � HL 10in � K12 � K10 � K8

� 0.013139 Q1.85 � 0.015936 Q1.85 � 0.04933 Q2 � 0.12058 Q2 � 0.031859 Q2

� 0.0291 Q1.85 � 0.202 Q2

Part 2: Modification of Pump Curve

Using the above equation for HL, a “modified” pump curve can then be developed by con-verting pump curve head values to include minor piping losses:

Q H (ft)

GPM CFS Uncorrected Corrected

0 0 200 200

1000 2.228 180 178.87

2000 4.456 160 151.52

3000 6.684 130 120.0

4000 8.912 90 72.29

The H values as corrected must then be plotted. The operating point of the pump is theintersection of the corrected H-Q curve with the system curve.

Part 3: Calculation of NPSHA

Using the data developed above for calculating the minor losses in the piping, it is nowpossible to calculate the NPSHA for the pump. Only the minor losses pertaining to the suc-tion piping are considered: Items 1–8 in Fig. 10.12. For this suction piping, we have: K12

� 1.96, K8 � 0.25, sum of C values, Pipe length for 12–in pipe: L � 26 ft.

Determine the headloss in the suction piping

HL � HL 12in � K12 � K8

� HL 12in � 1.96 � 0.25

� 0.013139 Q1.85 � 0.04933Q2 � 0.031859Q2

V�28

�

�2gV�

122�

�2g

V�28

�

�2gV�

122�

�2g

V�28

�

�2gV�

120�

�2gV�

122�

�2g

V�120�

�2g

V�28

�

�2g





� 0.013139 Q1.85 � 0.081189Q2

For Fig. 10.12, assume that the following data apply

High-water level � Elevation 2241 ft

Low-water level � Elevation 2217 ft

Pump centerline elevation � 2212 ft

Therefore:

Maximum static head � 2241 � 2212 � 29 ft.

Minimum static head � 2217 � 2212 � 5 ft.

Per Eq. (10.31),

NPSHA � hatm � hs � hvp � hL

For this example, use

hatm � 33.96 ft

hvp � 0.78 ft at 60°F

hs � 29 ft maximum

hs � 5 ft minimum

10.42 Chapter Ten

Compute NPSHA:

Condition Flow hs hatm hvp HL at Flow NPSHAat Flow(ft3/s) (ft) (ft) (ft) (ft) (ft)

High-static suction head 0 29 33.96 0.78 0.00 62.18

2 29 33.96 0.78 0.37 61.81

4 29 33.96 0.78 1.47 60.71

6 29 33.96 0.78 3.28 58.90

8 29 33.96 0.78 5.81 56.37

10 29 33.96 0.78 9.05 53.13

Low-static suction head 0 5 33.96 0.78 0.00 38.18

2 5 33.96 0.78 0.37 37.81

4 5 33.96 0.78 1.47 36.71

6 5 33.96 0.78 3.28 34.90

8 5 33.96 0.78 5.81 32.37

10 5 33.96 0.78 9.05 29.13




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