Grundläggande hydraulik Ove Isaksson
© Ove Isaksson 2017 Förlag: BoD – Books on Demand, Stockholm, Sverige Tryck: BoD – Books on Demand, Norderstedt, Tyskland ISBN: 9789176996355
INNEHÅLL 1
Hydrostatiska system ..........................................................................................................1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
Teorin för hydrostatik ............................................................................................................................1 Tryck ...............................................................................................................................................................1 Flöde................................................................................................................................................................2 Bernoullis ekvation ..................................................................................................................................3 Kraft- och rörelsestorhet.......................................................................................................................5 Effekt ...............................................................................................................................................................6 Verkningsgrad ............................................................................................................................................7 Hydraulsystemets uppbyggnad .........................................................................................................8 Historisk tillbakablick..........................................................................................................................10
2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19
Ledningar................................................................................................................................................... 13 Tank .............................................................................................................................................................. 13 Riktningsventil ........................................................................................................................................ 14 Styrning av riktningsventil................................................................................................................ 15 Tryckbegränsningsventil.................................................................................................................... 16 Pump ............................................................................................................................................................17 Cylinder.......................................................................................................................................................17 Motor............................................................................................................................................................ 17 Strypning.................................................................................................................................................... 18 Backventil .................................................................................................................................................. 18 Strypbackventil ....................................................................................................................................... 19 Filter, kylare och värmare.................................................................................................................. 19 Volymströmsregulator ........................................................................................................................ 20 Dubbelpump ............................................................................................................................................. 20 Snabbkoppling......................................................................................................................................... 21 Tryckkälla och manometer................................................................................................................ 21 Tryckvakt ................................................................................................................................................... 21 Tryckstegrare........................................................................................................................................... 22 Kopplingsschema ................................................................................................................................... 22
2
Symboler och kopplingsschema .................................................................................. 13
3
Omvandlare........................................................................................................................... 29 3.1 3.2 3.3 3.4
Pump/Motor............................................................................................................................................. 29 Deplacement............................................................................................................................................. 29 Verkningsgrad .........................................................................................................................................31 Omvandlarsamband cylinder........................................................................................................... 34
4
Angulära omvandlare ....................................................................................................... 39 4.1 4.2 4.3 4.4 4.5 4.6 4.7
Kugghjulsmaskin ....................................................................................................................................39 Icke evolvent kuggprofil och snedskurna kuggar...................................................................41 Vingmaskin ................................................................................................................................................42 Axialkolvmaskin......................................................................................................................................44 Radialkolvmaskin ...................................................................................................................................47 Långsamtgående hydraulmotor ......................................................................................................48 Vridmotor...................................................................................................................................................49
5.1 5.2 5.3 5.4 5.5 5.6 5.7
Cylinder.......................................................................................................................................................53 Genomgående kolvstång.....................................................................................................................54 Plungecylinder.........................................................................................................................................54 Teleskopcylinder ....................................................................................................................................54 Digitalcylinder..........................................................................................................................................55 Tätning.........................................................................................................................................................58 Avstrykare..................................................................................................................................................62
6.1 6.2 6.3 6.4
Ventilutformning ....................................................................................................................................65 Riktningsventiler utförande sätesventil......................................................................................67 Mittläge........................................................................................................................................................68 Pilotstyrd riktningsventil ...................................................................................................................70
7.1 7.2 7.3 7.4
Strypning ....................................................................................................................................................75 Likriktarplatta..........................................................................................................................................76 Flödesdelare..............................................................................................................................................77 Fyllventil .....................................................................................................................................................78
8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9
Tryckstyrd backventil ..........................................................................................................................79 Hydraullås..................................................................................................................................................79 Växelventil .................................................................................................................................................80 Sekvensventil............................................................................................................................................80 Avlastningsventil ....................................................................................................................................81 Tryckbegränsningsventil....................................................................................................................81 Pilotstyrd tryckbegränsningsventil...............................................................................................83 Externt styrd tryckbegränsningsventil........................................................................................83 Tryckregulator.........................................................................................................................................83
9.1 9.2 9.3 9.4 9.5
Hydraulvätskans uppgift.....................................................................................................................87 Viskositet ....................................................................................................................................................88 Viskositetsindex ......................................................................................................................................91 Tank ..............................................................................................................................................................91 Filter..............................................................................................................................................................93
5
Linjära omvandlare och tätningar .............................................................................. 53
6
Riktningsventiler................................................................................................................ 65
7
Flödesventiler ...................................................................................................................... 75
8
Tryckventiler........................................................................................................................ 79
9
Hydraulvätska...................................................................................................................... 87
9.6
Filtrerbarhet ............................................................................................................................................. 93
10.1
Ackumulator typer ................................................................................................................................ 95
11.1 11.2
2-vägsinbyggnadsventil ...................................................................................................................... 99 Monoblock uppbyggnad .................................................................................................................. 102
10
Ackumulator ......................................................................................................................... 95
11
Monoblock ............................................................................................................................. 99
12
Systemteknik..................................................................................................................... 109 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 12.10 12.11 12.12 12.13 12.14 12.15 12.16 12.17 12.18 12.19 12.20 12.21 12.22 12.23 12.24 12.25 12.26 12.27 12.28
Inledning ................................................................................................................................................. 109 Styrning.................................................................................................................................................... 109 Flödes- och tryckförsörjning ......................................................................................................... 110 System med fast deplacement ...................................................................................................... 111 Avlastningskrets .................................................................................................................................. 112 Ackumulatorsystem........................................................................................................................... 113 Flerpumpssystem................................................................................................................................ 116 Pumpstyrning ....................................................................................................................................... 117 Öppet och slutet hydraulsystem .................................................................................................. 117 Tryckkompenserad pump............................................................................................................... 119 Sekundärstyrning................................................................................................................................ 120 Ventilstyrning ....................................................................................................................................... 121 Inlopps-, utlopps- och shuntstrypning...................................................................................... 121 Antikavitationsventil......................................................................................................................... 124 Synkronisering eller parallellstyrning...................................................................................... 125 Ventilstyrning ....................................................................................................................................... 125 Seriekoppling ........................................................................................................................................ 127 Angulära maskiner som flödesdelare........................................................................................ 128 Mobila system....................................................................................................................................... 129 System med öppet centrum ........................................................................................................... 130 System med stängt-centrum.......................................................................................................... 132 Differentialkoppling........................................................................................................................... 132 Flertryckssystem................................................................................................................................. 133 Bromsning av angulär motor......................................................................................................... 134 Begränsning vid förbrukare........................................................................................................... 135 Sekvenssystem ..................................................................................................................................... 135 Hydraullås............................................................................................................................................... 136 Filterplacering ...................................................................................................................................... 137
13.1 13.2 13.3 13.4 13.5 13.6 13.7
Spaltströmning..................................................................................................................................... 149 Navier-Stokes ekvation .................................................................................................................... 149 Laminär strömning i spalt............................................................................................................... 151 Strömning i raka ledningar............................................................................................................. 154 Strypningar ............................................................................................................................................ 157 Engångsmotstånd................................................................................................................................ 159 Densitet.................................................................................................................................................... 161
13
Grundläggande strömningslära ................................................................................ 149
13.8 13.9
Kompressibilitet och tryckmodul................................................................................................161 Kylare ........................................................................................................................................................165
14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 14.10 14.11 14.12
Inledning..................................................................................................................................................175 Masströghet eller induktans ..........................................................................................................176 Fjädring eller Kapacitans.................................................................................................................177 Dämpning eller Resistans................................................................................................................178 Laminär strömning i rör...................................................................................................................178 Turbulent strömning i rör...............................................................................................................179 Viskös strypning ..................................................................................................................................179 Densitär strypning ..............................................................................................................................179 Hydraulisk styvhet..............................................................................................................................180 Dynamiken hos motor-last system .............................................................................................184 Transmission med växellåda .........................................................................................................186 Tryckspikar i hydraulsystem.........................................................................................................187
15.1 15.2 15.3 15.4 15.5 15.6 15.7
Flödesförsörjning ................................................................................................................................191 Försörjning vid nödläge ...................................................................................................................192 Balansering av statiska krafter .....................................................................................................192 Dämpning av tryck- och flödespulsationer.............................................................................193 Termisk expansion .............................................................................................................................194 Laddning- och urladdning av ackumulator.............................................................................194 Effektförbrukning................................................................................................................................196
16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 16.10 16.11 16.12 16.13 16.14 16.15 16.16 16.17 16.18 16.19 16.20 16.21
Pumpar med interna ventiler ........................................................................................................201 Tryckkompenserad pump...............................................................................................................201 Konstant flöde.......................................................................................................................................203 Pump med två styrkolvar ................................................................................................................205 Effektreglering ......................................................................................................................................208 Sekvensstyrd variabel pump .........................................................................................................208 Verkningsgrad.......................................................................................................................................210 Förlustmodeller....................................................................................................................................210 Volymetriska förluster......................................................................................................................210 Mekanhydrauliska förluster...........................................................................................................213 Viskösa modellen.................................................................................................................................215 Volymetriska förluster......................................................................................................................216 Densitär volymetrisk förlust..........................................................................................................216 Kompressionsförlust .........................................................................................................................216 Momentförluster..................................................................................................................................218 Viskös friktion .......................................................................................................................................218 Konstant friktion..................................................................................................................................219 Hydrodynamisk friktion...................................................................................................................219 Beräkning av konstanter..................................................................................................................219 Vriddon.....................................................................................................................................................220 Volymström från kolvpump ...........................................................................................................220
14
Dynamik ...............................................................................................................................175
15
Analys ackumulator ........................................................................................................191
16
Analys angulära omvandlare ......................................................................................201
17
Analys linjära omvandlare .......................................................................................... 229 17.1 17.2 17.3 17.4
18
Analys Cylindrar .................................................................................................................................. 229 Cylindermontering ............................................................................................................................. 229 Ändlägesdämpare ............................................................................................................................... 230 Knäckning ............................................................................................................................................... 232
Analys ventiler.................................................................................................................. 241 18.1 18.2 18.3 18.4 18.5 18.6 18.7 18.8 18.9 18.10
Riktningsventil ..................................................................................................................................... 241 Noll överlappning................................................................................................................................ 242 Excentriskt belägen kolv ................................................................................................................. 244 Lastinterferens ..................................................................................................................................... 247 Linjärisering .......................................................................................................................................... 249 Tryckbegränsningsventil................................................................................................................. 251 Volymströmsregulator ..................................................................................................................... 253 Backventil ............................................................................................................................................... 255 Avvikelser hos proportionalventil .............................................................................................. 256 Elektroniska styrkort ........................................................................................................................ 258
19.1 19.2 19.3 19.4 19.5 19.6 19.7 19.8 19.9 19.10 19.11 19.12 19.13 19.14 19.15 19.16
Dimensionering.................................................................................................................................... 263 Kravspecifikation ................................................................................................................................ 263 Kopplingsschema ................................................................................................................................ 263 Fysisk layout.......................................................................................................................................... 265 Cylinderdimensionering.................................................................................................................. 267 Dimensionering och val av pump................................................................................................ 269 Val av ledning........................................................................................................................................ 270 Val av ventiler ....................................................................................................................................... 273 Val av tankstorlek ............................................................................................................................... 274 Pumptryck .............................................................................................................................................. 275 Knäckningsrisk..................................................................................................................................... 275 Val av hydraulvätska ......................................................................................................................... 275 Totalverkningsgrad............................................................................................................................ 278 Val av kylare .......................................................................................................................................... 278 Val av filter ............................................................................................................................................. 278 Dimensionering av transmission................................................................................................. 279
19
Dimensionering och systemanalys.......................................................................... 263
20
Svar ........................................................................................................................................ 287
21
Sakregister.......................................................................................................................... 299
1 HYDROSTATISKA SYSTEM 1.1
TEORIN FĂ–R HYDROSTATIK
Hydrauliken och pneumatik behandlar energiÜverfÜring med ett flytande medium (fluid) i rÜrelse eller vila, dvs. vätska eller gas som energibärare vid energitransport. Redan 1588 publicerade Ramelli principen fÜr en axialkolvpump fÜr att pumpa vatten och Kepler kom med principerna fÜr kugghjulspumpen tidigt 1600-tal. Den franska matematikern Blaise Pascal gjorde dock de banbrytande insatserna inom hydrostatiken men det fick ingen stÜrre praktisk användning fÜrrän ca 100 ür senare. Omvandlingsprocessen frün fluid energi till mekanisk energi i ett hydraulsystem domineras av statiska krafter. Teorin fÜr hydrostatiken enligt Pascal ger, Figur 1-1:   
Trycket i en vätska i vila fortplantas sü att den blir densamma i alla punkter Trycket verkar lika i alla riktningar Trycket verkar i riktning vinkelrät mot varje yta som är i kontakt med vätskan eller i varje godtyckligt snitt genom vätskan
FIGUR 1-1 TRYCKSATT KĂ„RL
Detta innebär att vätskan anpassar sig till vilket kärl eller kärlsystem som helst, dvs. vätskor har ingen egen form utan formar sig efter kärlets väggar.
1.2
TRYCK
Tryck är en av de viktigaste storheterna inom hydrauliken. FĂśr att fĂĽ kraftjämvikt fĂśr kolven sĂĽ mĂĽste fĂśljande villkor vara uppfyllt: đ?‘?∙đ??´âˆ’0∙đ??´ =đ??š → đ?‘? =
1
đ??š đ??´
FIGUR 1-2 KRAFTJĂ„MVIKT FĂ–R KOLV
Trycket definieras alltsü som kraft per areaenhet, dvs. kraften är proportionell mot arean. Dess enhet i SI-systemet blir, [N/m2], Newton per kvadratmeter eller, [Pa], Pascal. Enheten har fütt sitt namn efter Blaise Pascal. Inom branschen används fortfarande ofta ocksü tryckenheten [bar]. 1 bar = 100 000 Pa = 0.1MPa. Trycket mäts ofta med manometer som är graderad i süväl MPa som bar. Normalt anger man inom hydrauliken Üvertryck, dvs. trycknivün i fÜrhüllande till atmosfärstrycket (oftast lika med tanktryck) som sätts till 0.
FIGUR 1-3 DEFINITIONER PĂ… TRYCK
Vid beräkningarna använder man sig alltsü av Üvertryck eftersom trycket oftast är i storleksordning 20 till 40 MPa och atmosfärstrycket (0.1MPa) kan dü fÜrsummas i sammanhanget. Vissa beräkningar inom hydrauliken kräver dock att man jobbar med absoluttryck, till exempel vid dimensioneringen av gasackumulatorer eftersom gaslagen tillämpas. Dessutom sü kan trycket lokalt i hydraulsystem vara under atmosfärstrycket, dvs. vi har dü undertryck i systemet. I sugledningen frün tank till pump kan det till exempel uppstü undertryck.
1.3
FLĂ–DE
FlĂśdet eller volymstrĂśmmen genom en kanal med tvĂĽ olika tvärsnittsareor är densamma i bĂĽda tvärsnitten, flĂśdeskontinuitet (densiteten konstant). Det innebär att vi fĂĽr fĂśljande samband fĂśr flĂśdet i de tvĂĽ tvärsnitten: đ?‘„ = đ?‘Ł1 ∙ đ??´1 = đ?‘Ł2 ∙ đ??´2
FIGUR 1-4 FLĂ–DESKONTINUITET
2
FĂśr en cylinder sĂĽ fĂĽr vi att hastigheten hos kolven blir đ?‘„ đ??´ Enheten fĂśr flĂśde blir [đ?‘š3 /đ?‘ ], ofta anger man dock flĂśdet i hydraulsystem i [đ?‘™đ?‘–đ?‘Ąđ?‘’đ?‘&#x;/đ?‘šđ?‘–đ?‘›]. đ?‘„ =đ?‘Łâˆ™đ??´ → đ?‘Ł =
FIGUR 1-5 SAMBAND HASTIGHET OCH FLĂ–DE
1.4
BERNOULLIS EKVATION
FĂśr en vätska med konstant densitet, dvs. inkompressibel, gäller vid stationär strĂśmning i rĂśr fĂśljande ekvation đ?‘Ł2 + đ?œŒ ∙ đ?‘” ∙ â„Ž = đ?‘˜đ?‘œđ?‘›đ?‘ đ?‘Ąđ?‘Žđ?‘›đ?‘Ą 2 där p är statiska trycket, đ?œŒ är densiteten, v är medelhastigheten och h är hĂśjdskillnaden frĂĽn referensnivĂĽn. Ekvationen kallas fĂśr Bernoullis ekvation. Ekvationen är giltig fĂśr en strĂśmlinje, men om man antar att konstanten har samma värde längs de olika strĂśmlinjerna kan ekvationen tillämpas fĂśr ett rĂśrtvärsnitt dĂĽ medelvärden används. Termerna i ekvationen ovan benämns: đ?‘?+đ?œŒ
đ?‘? = đ?‘ đ?‘Ąđ?‘Žđ?‘Ąđ?‘–đ?‘ đ?‘˜đ?‘Ą đ?‘Ąđ?‘&#x;đ?‘Śđ?‘?đ?‘˜ đ?œŒ
đ?‘Ł2 = đ?‘‘đ?‘Śđ?‘›đ?‘Žđ?‘šđ?‘–đ?‘ đ?‘˜đ?‘Ą đ?‘Ąđ?‘&#x;đ?‘Śđ?‘?đ?‘˜ 2 đ?œŒ ∙ đ?‘” ∙ â„Ž = â„ŽĂśđ?‘—đ?‘‘đ?‘Ąđ?‘&#x;đ?‘Śđ?‘?đ?‘˜
FIGUR 1-6 STRĂ–MNING I RĂ–R
3
Bernoullis ekvation säger att summan av statiska trycket, dynamiska trycket och hĂśjdtrycket är konstant längs ett rĂśr vid friktionsfri, stationär och inkompressibel strĂśmning. I hydrostatiska system är lägesenergin i allmänhet helt fĂśrsumbar jämfĂśrt med tryckenergin, dvs. hĂśjdtryck kan fĂśrsummas i fĂśrhĂĽllanden till statiska trycket. Detsamma gäller fĂśr den dynamiska termen att den kan fĂśrsummas i fĂśrhĂĽllande till den statiska. I verkligheten uppstĂĽr alltid fĂśrluster, varfĂśr uttrycket kan skrivas đ?‘Ł12 đ?‘Ł22 + đ?œŒ ∙ đ?‘” ∙ â„Ž1 = đ?‘?2 + đ?œŒ + đ?œŒ ∙ đ?‘” ∙ â„Ž2 + ∆đ?‘?đ?‘“ 2 2 där ∆đ?‘?đ?‘“ är tryckfĂśrlusterna mellan de tvĂĽ sektionerna. FĂśrlusternas storlek kan uppskattas och kommer att tas upp under avsnittet rĂśrstrĂśmning. đ?‘?1 + đ?œŒ
EXEMPEL 1-1
I ett rĂśr strĂśmmar hydraulvätska, Figur 1-7. FrĂĽn sektion 1 till sektion 2 minskar tvärsnittsarean frĂĽn 0.003 đ?‘š2 till 0.0015 đ?‘š2 . I sektion 1 är medelhastigheten 1.8 đ?‘š/đ?‘ och det statiska trycket 117 đ?‘˜đ?‘ /đ?‘š2 . Bestäm trycket i sektion 2 under fĂśrutsättning att friktionens inverkan fĂśrsummas. Sektion 2 ligger 6 m ovanfĂśr sektion 1 och densiteten hos hydraulvätskan är 965 đ?‘˜đ?‘”/đ?‘š3 . Medelhastigheten i sektion 2 blir: đ?‘Ł2 =
đ??´2 0.003 đ?‘Ł1 = 1.8 = 3.6 đ?‘š/đ?‘ 0.0015 đ??´1
Friktionen fĂśrsummas, dvs. ∆đ?‘?đ?‘“ = 0 đ?œŒ 965 (1.82 − 3.62 ) đ?‘?2 = đ?‘?1 + (đ?‘Ł12 − đ?‘Ł22 ) + đ?œŒđ?‘”(â„Ž1 − â„Ž2 ) = 117000 + 2 2 −965 ∙ 9.81 ∙ 6 = 56 đ?‘˜đ?‘ /đ?‘š2
FIGUR 1-7 FRIKTIONSFRI RĂ–RSTRĂ–MNING MED HĂ–JDSKILLNAD
4
1.5
KRAFT- OCH RĂ–RELSESTORHET
FĂśr att lyfta lasten, Figur 1-8, applicerad pĂĽ den hĂśgra cylindern med en given hastighet krävs ett flĂśde frĂĽn den mindre vänstra cylindern. FĂśr att flĂśdet ska uppstĂĽ mĂĽste det skapas ett tryck i den hĂśgra cylindern som fĂśrmĂĽr lyfta lasten, dvs. Ăśvervinna kraften đ??š2 . I ledningen mellan cylindrarna kommer det att uppstĂĽ ett flĂśde när lasten fĂśrflyttas. Om man antar att fĂśrlusterna i ledningen är fĂśrsumbara kommer trycket i bĂĽda cylindrarna att vara lika.
FIGUR 1-8 PRINCIPEN FĂ–R HYDROSTATISK ENERGIĂ–VERFĂ–RING
FÜljande begrepp infÜrs: 
Kraftstorheter; I det mekaniska systemet utgĂśrs det av kraft (moment) och i det fluida systemet av tryck

RĂśrelsestorheter; I det mekaniska systemet utgĂśrs det av hastighet (varvtal) och i det fluida systemet av flĂśde FĂśr domkraften ovan fĂĽr vi idealt fĂśr kraftstorheterna att: đ??š1 đ??š2 =đ?‘?= đ??´1 đ??´2 AlltsĂĽ: đ??š2 =
đ??´2 đ??š đ??´1 1
och fĂśr rĂśrelsestorheterna att: đ?‘Ł1 ∙ đ??´1 = đ?‘„ = đ?‘Ł2 ∙ đ??´2 AlltsĂĽ: đ?‘Ł2 =
đ?‘Ł1 ∙ đ??´1 đ??´2 5
Analysen ovan är ideal. När problemet behandlas idealt sü kan vi notera att kraft- och rÜrelsestorheter är separerade. I verkligheten har vi büde läckage och friktion och dü blir sambanden ovan oftast kopplade, dvs. rÜrelsestorheterna püverkar kraftsambandet och vice versa. EXEMPEL 1-2
Vilket tryck mĂĽste idealt verka pĂĽ kolven, se Figur 1-9, fĂśr att ändra hastigheten hos en massa pĂĽ 1000 kg frĂĽn 0.3 m/s till 0.6 m/s pĂĽ 1 s. Kolvdiametern är 50 mm. Kraftjämvikt ger: đ??š = đ?‘šâˆ™đ?‘”+đ?‘šâˆ™đ?‘Ž =đ??´âˆ™đ?‘?
FIGUR 1-9 DYNAMISK JĂ„MVIKT FĂ–R KOLV
AlltsĂĽ: đ?‘Ž=
đ??´âˆ™đ?‘?−đ?‘šâˆ™đ?‘” đ?‘‘2 ∙ đ?œ‹ = đ?‘˜đ?‘œđ?‘›đ?‘ đ?‘Ąđ?‘Žđ?‘›đ?‘Ą, đ?‘‘äđ?‘&#x; đ??´ = đ?‘š 4
Konstant acceleration ger: đ?‘Ł(đ?‘Ą) = đ?‘Ž ∙ đ?‘Ą + đ?‘Ł0 đ?‘Ł = 0.3 đ?‘“Ăśđ?‘&#x; đ?‘Ą = 0 → đ?‘Ł0 = 0.3 đ?‘Ł = 0.6 đ?‘“Ăśđ?‘&#x; đ?‘Ą = 1 → 0.6 = đ?‘Ž ∙ 1 + 0.3 AlltsĂĽ a=0.3. Vi fĂĽr nu: đ?‘? = (0.3 + đ?‘”)
1.6
4∙đ?‘š = 5.15đ?‘€đ?‘ƒđ?‘Ž đ?‘‘2 ∙ đ?œ‹
EFFEKT
Effekten i ett vätskeflĂśde är pďƒ—Q, där p är trycket hos hydraulvätskan och Q är flĂśdet eller volymstrĂśmmen. FĂśr att illustrera detta kan vi betrakta cylindern i Figur 1-10. FĂśr att skjuta kolven ĂĽt hĂśger sträckan y krävs arbetet Fďƒ—y av hydraulvätskan. Effekten är arbete per tidsenhet, dvs. effekten blir: đ?‘ƒ=đ??š
đ?‘‘đ?‘Ś =đ??šâˆ™đ?‘Ł đ?‘‘đ?‘Ą 6