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2.2.Idealandrealcharacteristicsofapumpandamotor
27
ancesGinthepump,formedbetweentherotatingdisplacementchamberTand
thefixedelementsofthehousing.Hence,Figure2.5adepictsthecharacteristicsofreal
deliveryQ
gdependingontheloadofthepump∆p
g,namelyQ
g±f(∆p
g).Thecharac-
teristicsresemblestheshapeofaparabola.BetweentheoreticalcharacteristicsQ
gtand
realcharacteristicsQ
g,volumetricloss∆Q
gismarked.Figure2.4bshowsthatthe
streamindicatingtheoreticaltorqueM
gtisincreasedbyhydraulic-mechanicalloss∆M
g
and,asaresult,theshaftofthepumphastobeloadedwithrealtorqueM
g.Hydraulic-
mechanicalloss∆M
gtorqueresultsbothfromtheresistanceoftheworkingfluidflow
throughthechannelsandtheclearancesinthepump,andthefrictionbetweenthose
partsofthepumpwhichremainintherelativemotionduringtheoperationof
thepump.Takingthatintoconsideration,Figure2.5bpresentsthecharacteristicofreal
torqueM
gdependingonpressure∆p
gworkingonthepump,namelyM
g±f(∆p
g).
CharacteristicM
gisstillastraightlinebutitisshiftedrelativetothecharacteris-
ticoftheoreticaltorqueM
gtbythevalueoftorqueloss∆M
g.
TheanalysisofFigure2.5aallowstoobservethefollowingdependency:
Q
g±Q
gt-∆Q
g
(2.6)
Thefigureshowsthatvolumetricloss∆Q
ggrowsproportionallytothegrowthof
pressure∆p
gworkingonthepump.Itresultsfromthetheoryofflowthrough
theclearances,whichstatesthattheflowthroughtheclearancesofthedisplacement
chamberandvolumetricloss∆Q
ggrowproportionallytothegrowthofthepressure
difference∆pinsideandoutsidethedisplacementchamber.
ByjuxtaposingrealdeliveryQ
gwiththeoreticaldeliveryQ
gt,thevolumetriceffi-
ciencyofthepumpcanbedefinedas:
K1
vg
Q
Q
gt
g
1
Q
gt
Q
-'
gt
Q
g
(2.7)
TheanalysisofFigure2.5ballowstothedeterminethefollowingdependency:
M
g±M
gt+∆M
g
(2.8)
Thefigureshowsthatlosstorque∆M
ggrowsalongwiththegrowthofpressure
∆p
ginthepump.Thisoccursmainlyduetoanincreaseinthemechanicalfrictionand
anincreaseintheresistanceoftheworkingfluidflowinthechannelsofthepump.
ThecomparisonoftheoreticaltorqueM
gtwithrealtorqueM
genablesthedeter-
minationofthehydraulic-mechanicalefficiencyofthepump:
K
hmg
1
M
M
g
gt
1
M
g
M
-'
g
M
g
(2.9)
Consideringtherealpumpasamachinewhichcollectspowerfromthemotorand
transfersittothehydraulicsystem,itisnecessarytodeterminethepowerbalance.