., ..... . .. . mY". qtfa~;~doperating cost is..•... '. ;tile essentialrequirem~ntwhen desjgnip.g the. discharge

.... , piping for a' pump.' This: contrasts with the need for..re\iableope~tion when sizing the suction piping.

..IHhe '. ugal pump receives saturated liquid on thesuction the liquid. becomes well subcooled in the

..' . discharge me,; due to the increased pressure. This is one, ..';. reason why filtbrs,.orifice rUns, ./ron9'ol valves, exchangers,'a!'ld other flow'res~rietorsat:epl~don the discharge side

, of process :pumps.;,., :""".,;., '',fn this article, we Will analyze and compute the resist­

."ances to flow on the discharge side of the process pump.'. :"',As a rule, we 'can readily select economical sizes for

•',•.'.. discharge pipe ,up to about 12-in dill,. For larger diame­" iers;we must often make 'it more-detailed cost compari­

, . Son, in order 'to ,choose between alternative discharge-pipe des' ' . , J', .. '

"

By reviewing typical pump dala and'knowing only theflo""rate,we can readilyindicate a reasonable design forthe •. hydraUlic. system," regardless of discharge-pressurerequitementsof the pumped liqui~.

PerformanceCurves-'-ln Fig.l;wefind a compositerating '. chart' for a •. series Or standard chemical-processpumps; and the head-capacity curve for a specific pump.The performance curves for this pump show that it issuitable for h~ndling flmvs frmn150 to 300 gpm (close

CHEMICAL ENGlNl:ERfNG1MAY 26. 1Q7S

Flow, gpm •.......Impeller diameter, in ..Power,hp.. , , .. '.' :.>;.. 3 to 10Efficiency, % ." , ,...•:...,58 to-67Total head, ft water. " .........•... 3()to 9(j

All these data were obtained from Fi~.lbfo;thfhaving a 4-in suction nozzle and a3-in discharge nozzle.The total head repre.sents a differential pressure ofPto 39 psi (when pumping water) between sllction anddischarge flanges.

For a flow of about 250 gpm, the suction-pipe size canbe 6 in, the discharge pipe 4in.The orifice run can be .4 or 6 in, the control-valve size 3 or 4 in; block valvesand strainer should be line size. With these data, detailedcalculations can be made, pump total-head requirementdetermined, .and impeller. diameter and motor size se­lected.

A centrifugal· pump is adynamic. machine that canperform only on points on the head-capacity curve. Con­sequently,the sum of piping and components resistancesduring operation must fall exactly on the head-capacitycurve. The relationship between the pump's head­capacity curve and pipe-system resistance is shown inFig. 2. Resistance of the throttling valve sh?uldnot beincluded as part of the' system resistance. Tii(;'gap be­tween the head-capacity curve and the system-resistancecurve is available for throttling resistance (i.e., control­valve;),.P). While pipe resistanceincreasfis with higherflowrate, throttling resistance decreases. Or, at higher

113

CE I:lEFRESHER •..

PERFORMANCE of a typical series of centrifugal pumpsand detailed characteristics of the selected pump-Fig. 1

flowrates, the throttling valve has to open and pass largerflows with less resistance.

In manufacturers' head-capacity curves, the "TotalHead" usually does not include velocity-head differencescalculated between suction and discharge flanges. Thosediagrams that include velocity-head differences indicate"Total Dynamic Head" on the vertical scale. In this case,velocity-head differences should be added to the total­head calculations.

In a great number of publications, the head-capacity

114

...The curves in this drawing suggest that when the dis­

charge is throttled, the system-resistance curve moves toanother position. Not so! Only one system-resistancecurve exists for a given discharge line.' The. varying.M'of the control valve brings the system resistance up toa point on the head-capacity curve.

Head-capacity curves are. drawn for. pumping water.However, a centrifugal pump with a given impeller,speed and size will develop the same head in feet, nomatter what the liquid or specific gravity-providingviscosities are normal. Tile static-headpressure at thepump nozzles will be. higher with a h~avier liquid, an4the horsepower requirement will also increase. Brake­horsepower requirements for pu1tlpingwaterar~ super"imposed on the head-capacity curye(seeFig.lb). Wemultiply the horsepower reqpired top~mp ~aterby .thespecific gravity of the liquid being pumped to obtain

.actual ..• brake. horsep?wer,. Efficiency Cllrves are •.....alsosuperimposed on ,the head-capt;lcityCUt'Yes(Fig.lb). Theideal, normal. operatitlgpoi11tisitt.}h~m~um em-

. ciency range' JJ ' •••.. "'i"«:When calculating total-head require1l.1,ents atalterna­

live capacities, it is useful to know the operating points

In this case, the 4-in size isr~asonable for tlledis­charge pipe. The unit loss of a 3-in pipe will, rnost prob­ably, increase utility cost to an extent that cannot becompensated for by lower capital <:ost8 of the pipelineand components. And the cost of a possibly larger purnpand motor has not been taken into account. The unit lossof a 6-in pipe is far too lowfor an average process purnp.Where the discharge line is very long, a·6-in line rnightbe reasonable, such as thecopting-water supply headerto a distant point. .. .. .. .. ... .. ....•..

An example will best illustrate theconceptsJ()r calcu­lating the pump's differential pressure: ... .. . .... A pump moves a liquid having a density, p, of50 lb/ft3

from an overhead drurn loan elevated point00 a col-umn,'assketched here:

Total-Head Calculations

We can use the data plotted in Fig. 4 for selecting asuitable size for the dischargepiping·of a·· centrifugalpump. The shaded zones. in Fig. 4 will help in selectingeconomical sizes for alloy or carbon-steel piping in thecase of electric-motor or stearn-turbine drives.· ...........•

In general, economical sizes for discharge pipescan ..be easily recognized if we list the unit losses for severaladjacent pipe sizes. For example, the unit losses in .aSchedule 40 pipe for a 300-gprnflow, as obtained frornFig. 4, yield: .

MAY26,1.915fCHEMICALf:NGINEERING

where Q, Hand E are capacity, total head, andefficiency,.respectively, and wheresubscriptw stands for water, andsubscript vis stands for viscous liquid.

TwocPhase Flow-If the pressure drops below thevapor pressure of the liquid inllie discharge tine (forexample, after a heat exchanger. ora control valve),vaporization will occur. Friction resistance in the pipeincreases considerably. with the increased vapor contentof the liquid. This section of the discharge pipe shouldbe calculated for two-phase flow: If two-phase flow is

. expected in a pipeline between two pieces of process.equipment, capital cost and operating cost can be re­duced by locating this equipment side by side. Generally,lines with two-phase flow should be short.

CE REFRESHER . ..

Q w X CQ = Qvis

Hw X Co = HvisEw xCE = Evis

116

on the head-capacity curve, so that the available con­trol-valve pressure differentials can be more closely esti­mated.

If a pump has not been selected, we can still estimatethe increase in total head for a given pump when capacitydecreases by X% from a given capacity.. This increase intotal head can range fromO.S to 1.0 multiplied by X%.A high value for this increase (selected from the range

• 0.5 to 1.0), say 0.85X%, is justified for three reasons:1. The pump will notbe undersized.2. The head-capacity curve fof· a worn impeller will

have a more pronounced decline with increasing flow ascompared with a new impeller.

3. A somewhat increased control-valve ;j,P will providea more desirable plug position· at a maximum flow.

Viscous Flow-Areduction in head, capacity and effi­ciency, and an increase in horsepower,will occur whenpumping viscous liquids instead of water. (NPSH re­quirement does not change.) Fig. 3 shows a perform­ance~correction chart for conventional, single-stage, cen­trifugal pumps handling viscous Newtonian liquids forcapacities between 10 to 100 gpm. A similar chart isavailable for 100 to 1,000 gpmin the "Hydraulic InstituteStandards" [1].

These charts should not beused for multiple-impeller,mixed-flow and axial-flow pumps, or for pumps withspecial hydraulic design. Manufacturers can supply vis­cosity~correction charts for their pumps.

To use Fig. 3, we select a pump from the' manufac­turer's head-capacity curves at optimum efficiency, andnote the head,capacity and efficiency. We enter Fig. 3with the same capacity..We intersect the head line, infeet, and move horizontally left or right to viscosity; thenvertically up to intersect the· efficiency-correction factor,CE,capacity-correction factor, CQ, and head-correctionfactor, Cn. An example isdrawn in Fig. 3:

The corrected performance characteristics for viscousflow will be: .

Discharge,Psi

P2 = 15Pm = 10/),P2 =-.2.

34

Suction,Psi

PI = 10PHI = 5/),PI = .::i

14

Vessel pressureStatic-head pressureFriction loss

Total

We now subtract the total suction resistance from thedischarge line backpressure totind the· pump's differ­ential pressure excluding the control valve: 34 - 14 =20psi. Choosing a control~valve !:J.Pcv of 5 psi, we must addthis to the pump's differential pressure of20 psi to obtainthe total differential pressure across the pump flanges as

117

components resistances vary with flowrate (see Fig. 2).The analysis, therefore, becomes:

Pressurein the drum, 1'1' is lOpsi,and pressure inthe column, P2 ,is 15 psi. Pressure drop across the controlvalve, APw , equals S psi; and the friction losses in thesuction and discharge lines are Apl == I psi and Ap'i =9 psi, respectively. Let us calculate the required totalhead for the pump, i.e., the differential pressure, !:J.P,between the suction and discharge flanges.

Both suction head and discharge head consist of fourcomponents: static head, pressure head, velocity head,and piping and. components resistance. Velocity-headdifferences normally do nOt have tobe calculated becausethey are taken into account by U.S. pump manufacturersin their published. head-capacity curves. Pressure andstatic head in Ii systemusuaIly remain constant withchanging capacities.. Suction-pipe, discharge-pipe and

CHEMICAL ENGINEERINGlMAY 26, 1975

UNIT ,pressure losses In new, commercial-steel pipe help in selecting suitable sizes for discharge piping-Fig. 4

, . - ~'.

We then find. the eqUivalent length for the suction lineand its fittings from j:!ata in Part 2 ()f this series (Chern.Eng., Jan. 6, 1975, Tables I to IV): '

Pipe length . .5 Short-radius elbows .;.: ~ . : •.. '. . . 75 ftI Reducer .;'. ; .. ;.. .; . . .. .:; . ~ . .. 4 ft1 Strainer .. ... i •.;' ..;. . .. .-::, ...• , .. '. 30 ft1 Gate valve . •. ;. .' : .:.... . . 6.5 ft1 Inlet to pipe.·.·: .: •. ~:.:.~.. . 18 ft

Total equivalent length, .L, : ...:. . . . . 172.5 ft

Hence, the overallioss for the line and its fittings atthe normal flow of 250 gpm becomes;·

I:l.P = I:l.Pl00(LllOO~ • ' ...•.•.. ..'I:l.P'~ 0.19(172.5/100) = 0.:33 psi at normal flowI:l.P = 0.33(250/275)2 ::::0.4 psiat maximum flow

. MAY 26, 1:97~/CHEMICA'L ENGINEERING

...

Discharge Line4

4.0261,058

Suction Line6

6.0658,206

H = (25)(144)/50 = 72 ft

Nominal size,.inInsidedia., d, ind5

Example Illustrates Detailed Design

25 psi, or expressed ashead of liquid (the required totalhead):

Suction-Line-We fine the loss in the suction line by

118

A centrifugal pump having a 4-insuction nozzle anda 3-in discharge nozzle will handle a gas oil at a normalflowrate of 250gpm through a piping and componentssystem, as d.rawnin Fig. 5. Allowing for a safety factorof l.l, we' find that the maximum flowrate will be1.l(250) = 275 gpm.Specific gravity and density are:S60 = 1.18" and P60== 73.6 Ib/ft3, respectively. At theflowing temperature o[555°F,S =1.04 andp= 64.87Ib/ft3.. Viscosity of the gas oil is O.Gep. There isa flowcontrol valve in the discharge line.

Letus calculate the total head on the pump whenitis expected to operate ata normal flowrate and at' amaximumflowrate.

We will begin the analysis by first determining the lossin the suction .line and then that in the discharge line.

.Pertinent data for the Schedule 40 pipe are:

tE REFRESHER . ..

"5. C), b

50.40

1

+ 5.'2 c

Discharge pressure ........•.... (:+ 58.34 55.51-

Suction·nozzle pressure j Ia.97 - '8."

Pump differential pressure ......•.... '1 39·37 36.6tRequiredtotalhead,(144xAPI/p..... 87.'1- eft----- a'.3 ft

.Total head from head-capacity curve. . • . ..2Lft

Total-head safety margin. .. •.•• .. . 10.7 ft

.aOther equipment resistance...bPump safetV factor,s.f." 1.l.·With C..,IC. = 1: .dWith Cve/C. = 0.5 to 0.8eAHlnormal flow) = AH (maximum flow)" J.:.E.:!§.

dl.3)( '.075 "87.4

119

For this defiection, we can use a 100- or 125-in-longmanometer. The orifice I:1Po will be:

t.P.= 6.73(62.37)/144= 2.92 psi

With (3 =0.7, the permanent loss will be 52% of theorifice pressure differential.*

APo(loss) = 0.52(2.92) = 1.52 psi

Line 4: Friction loss in the discharge (and suction) linehas been previously computed as 6.47 psi. Line 5: Pres­sure drop through the exchanger (and other equipment)can be obtained from the manufacturers. Line 6 is thesum of Lines 3 to 5 at the normal flowrate.. For a 10%greater fiow and a pump safety factor of 1.1, resistanceof the discharge line will increase by (1.1)2. Line 7 isthe subtotal of Lines I, 2 and 6 at normal flow and atmaximum fiow.

At this point, we. will continue the calclllations at themaximum fiowrate for reasons that will become evident.

Line 8: For the control valve to operate in an optimum.. range at normal flow, weusually consider the valve plugC . in afully open position at maximum flow. This also gives

a minimum pressure drop through the control valve t . A4-in single-seat control valve has a valve coefficientt

Cv = 124. And, withCvc/Cv = 1:

liP -[ Q "fS(min) - (Cvc/Cv)Cv J

!J.P _[~"f(min) - 1 X 124 JI.04 = 5.12 psi

Line 9 is the required discharge pressure, includingcontrol-valve I:1P at maximum flow. Suction-nozzle pres­tFor det~i1s, see Part 5 of this series, Chern. Eng.• Apr. 14, 1975, p. 89.

To fin4 the pressure at the suction nozzle, we calculatethe static-head pressure: (14)(64.87)/144 = 6.3 psi, andadd this to the vessel pressureof 13 psito get 19.3 psi.Since the pipe-friction loss ·atnormal.flow is 0.33 psi,the pressure at the suction nozzle becomes 19.3 -'­0.33 =18.97 psi.. At maximum fiow, the pressure at thesuctioQ nozzle is 19.3 -'-0.4, or 18.9 psi.Discharge-Line~We now perform similar computa­

tions to find the loss in the discharge line. Therefore, forthe discharge line;<

NRe = sO.6c250/4.026)(64.117jCl.6) = 340,000

The friction faethr,/. for this Reynolds number is0.0178· from charts in· Part 1 of this series. We now useFig. 4 to find the unit loss, I:1P100' as 1.32 psi for totallyturblllent conditions at the normal flow of250 gpm. Sincethe fiow for this Reynolds number is in the trallsitionalregion (see Part I of this series, Chern. Eng.,I>ec. 23,1974, p. 65), we must correct the unitlQss as follows:

t.P1OO = 1.32(1.04)(0.0178/0.0165) = l.48 psi/loo ft.We then find the equivalent length for the discharge

and its fittings from datain Part 2 of this series:

Pipe length;:.. ; 15Mt20 Short-radius ..•. 210 ft4 Gate valves. i8 ft

'I Reducer. . . 3 ft

2 Exits .... ! .'; .;... .... .•. .•. .......•..........• .... ...... 40 ft1 Inlet .. , .......•....... ,.:;:.:..... . 10ftTotal equivalent length, £; .. >;:.; .....• 437 ft

Hence, the overall loss for theliIle an4its fittingsat th~··normal flow of 250 gpm b~comes:

t.P= AP1OO(L/IOO)AP =1.48(437/100) =6.47 psi

liP = 6.47(275/250)2 =7.83 psi

A detailed, specific and systematic procedure is shownin Table I for calculating the total head on the pump whenit operates at a normal fiowrate and at the maximumflowrate.

For the calcmations presente4in Table I, the followingsteps are recommended: ..

Lines 1 to 6 can be worked out simultaneously fornormal and maximum. flow. Lines land 2: Discharge­vessel presstireand discharge static head do not changewith alternative flow capacities. Lines 3, 4 and 5: OrificeI:1P, pipe-friction loss, and equipment-friction loss in­crease with capacity. Hence:

AP_=: (Pl4mpSafety Factor?APlIOrmal

h",= [O.l76Qv'S/(dlfJ~C)]~

h",= {0.176(250)VT.04/(l6.21 X 0.339)]2h", = 80.7 in, or 6.73 ft

sure has been previously computed. By deducting thesuction·inlet pressure from the required discharge pres­sure, we obtain the pump's differential pressure at maxi­mum flow (Line 11). This is conyerted to the equivalenthead (Line 12) at maximum flow by using the previouslydetermined value of 36.62 psi from Table I:

144(~P) = 144(36.62) = 81 3fp 64.87 . t

Let us now summarize some of these results. Thepressure needed at the pump-discharge nozzle to over~

come backpressure in the discharge line isthe sum(Line 9 in Table I) of actual pressure in the dischargevessel, static-head lift up to the terminating nozzle (orliqUid .level in discharge drum), control-valve D.P, andtotal discharge-pipe and equipment resistances. Pumpdifferential pressure (Line 11) equals discharge pressure(Line 9) minus suctiori-nozzleptessure (Line 10). .

We can now estimate the total head at normal flowrate.Total head will increase by an amount ranging from 0.5to 1 of the percentage decrease in capacity. In this ex­ample, there is a 10% decrease incapacity. Hence, for'a single-impeller pump, we will assume an increase inthe total head of about 7.5% (i.e;, 0.75 of 10%). Thecomputed value is on Linel2 for the normal flow. Cal­culated values for the total head for this example areshown in Fig. 1b.

Suction-nozzle pressure at normal flow is on Line 10.. Line 9 = Line 10 + Lind I;

The available pressure differential at normal flow forcontrol-valve sizing (Line 8) equals discharge pressure(Line9) minus the line backpressure without the controlvalve (Line 7). This D.P should give a control~valve co­efficient falling within' the recommended ranges ofCve/Cv =0.5 to 0.8 for equal-percentage contouredplugs:

eve = QVSi....rs:P= 250(Vl.04)tvlO.71) =77.9

For the selected 4-incontrol valve, CvclCv =77.9/124,or 0.63, which is acceptable.

For a normal flow of 250 gpm and 87.4ft total headon the one hand, and a maximum flow of 275 gpm and81;3 ft on the other, we can now select the pump, as shownin Fig. I; Impeller diameter for the selected pump is10 in, and a standard motor of 10 bhp is required. Themotor will work with abetter. than 65% efficiency.

The calculated, total-head points fall between the 9­and lo'"-in impellers. The pumpWill operate at 95-ft totalhead at 250 gpm, and at 92-ft at 275gpm. The extrahead (7.6 and 10.7 ft, respectively, here) provides a safetymargin compensating for inaccuracies in the' assessmentof the flow-properties and line data. These additionalpressure differentials can be absorbed' by the controlvalve. Or, the block valve in the discharge line can beslightly closed to bring the operating point up to thehead-capacity curve. Also, the motor will be able to drivethe pump when the liquid is colder and specific gravitiesare greater than at operating conditions.

If a pump has not been selected and the head-capacitycurve is not available, a safety margin of 5 to 15% canbe estimated and added to the required total head ofLine 12.

120

-r,~~':~'r;,"~';ft:-,;';

As thci data in Fig. Ib sho~.se~eralsizeso it1lpellers.;can be placed in one pump case. The.cost difference' .....between impeller sizes is negligible. MotOr sizes are usu-: '.' '.ally well determined. A difference in the cost of the pump' .and motor occurs for pumps falling in adjacent envelopes" ..of the composite rating chat!. In some bordemne cases; '.,it may be more economicalJo. redesign.the'discharge .•..piping for lower pressure drop rtther,Jhai}to invest i~'a larger pump and motor.'.' '.: •....';'~( .' ...~ ... :. •.....•. , :

For economy in utility cost,the.primpshoukl work atits highest efficiency.' High putnpefficiencyresultsin .

.minimum horsepower input, and' lilinimum wear. and' ,maintenance. High-efficienty pumps .. last longer, are .. •..•quieter and vibrate less than low-efficiency ones{21.. '·

Small pumps should not· be oversized. 'the total ofoversized small motors in a plant can add to substantialwaste in energy usage. .. .. ' .' .' .' .' .',,

For pipe diameters above 12 in, more than one Sizemay be selected initially because capacity increments inlarge-size pipe are very close.. Piping costs,. of course,increase with diameter, while utility costs decrease.be­cause of smaller pipe .and componentsresista11ces~The.,best size can be determined by adding the totalcost of'utilities over the period of capital payout ;io~ theccist of.the mechanical and electrical installation:. The. lowesttotal cost calculated for a 2-, 5~ or 10-:yr '~mdrtization • •will give the most economical design. ", .<'; .

A detailed investigation for the' most'.econolillcat pipesize is justified if line sizes are large, pipe ~nfigurations

are long or complicated, or if the pipjrig material isexpensive. Pipe friction must contribute a major portionof the discharge pressure-otherwise, there will be littledifference in total heads between alternative designs.Actual vessel pressures and static liqui4 heights usuallycannot be altered. '.c:' '. ' ''''., .'

For reciprocating pumps, the avaiIableNPSH, pumpdifferential pressure, suction-line and discharge-line re­si'stances cannot be calculated' in the same way as forcentrifugals. Because of pulsating flow, the minimum­pressure levels should not fall below the vapor pressurewhen saturated liquid is pumped. For identicalflowrates,pressure losses in suction and discharge lines of recipro­cating pumps are greater than in those of centrifugal

.pumps. These principles have beenadequately discussedby Hattiangadi [3]. For information on power ratings,installation and operation ofrecipr9cating pumps, con­sult the "Hydraulic Institute Standards" 14]. The Stand­ards [4] also contain information on electric-~otor-driven and steam-driven reciprocating pumps. .

The next article in this series will appear in the issueof June 23, 1975,and will reviewpiping design for two-phase (i.e., vapor-!iquid) flow: # . .

ReferencesL ."Hydniulic Institute Stand~rds," 12th ed,p. 81; Hydraulic Institute,

New York, 1969..2. Marischen; J. P.,,,Cri\ical Centtifugal Pump Iriformation," Ampco

Metal Inc., Milwaukee, WI 53201.' .... .... .,...3.' Hattiangadi; U. S.;Specifying CenttifugalandReciproeating Pumps,

Chern. Eng., Feb. 23, 1970,pp.lOI.c108, ....4. "Hydraulic InstituteStimdards," 12th ed. pp.165-166, 181:"182,204­

205, Hydraulic Institute,New York;'1969.';···· c.