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ME3333Thermodynamics

HWIV_Solution,Fall2010

232E

Theworkrequiredtocompressaspringistobedetermined.

Analysis Sincethereisnopreload,F=kx. Substitutingthisintotheworkexpressiongives

[ ]

Btu0.0107

ftlbf8.33

=

=

=

=

====

ftlbf169.778

Btu1ft)lbf33.8(

in12

ft10)in1(

2

lbf/in200

)(2

22

21

22

2

1

2

1

2

1

xxk

xdxkkxdxFdsW

238 Acaristoclimbahillin12s.Thepowerneededistobedeterminedforthreedifferentcases.Assumptions Airdrag,friction,androllingresistancearenegligible.AnalysisThetotalpowerrequiredforeachcaseisthesumoftheratesofchangesinpotentialandkineticenergies.Thatis,

ga WWW&&& +=total

(a) &Wa = 0 sincethevelocityisconstant.Also,theverticalriseish=(100m)(sin30)=50m.Thus,

kW.047s)/(12/smkg1000

kJ1m))(50m/skg)(9.81(1150/)(

22

212 =

== tzzmgWg&

and kW47.0=+=+= 0.470total ga WWW &&& (b) Thepowerneededtoaccelerateis

( )[ ] kW1.43s)/(12/smkg1000

kJ10m/s30kg)(1150

2

1/)(

2

122

221

22 =

== tVVmWa&

and kW90.1=+=+= 1.430.47total ga WWW &&& (c) Thepowerneededtodecelerateis

( ) ( )[ ] kW5.57s)/(12/smkg1000

kJ1m/s35m/s5kg)(1150

2

1/)(

2

122

2221

22 =

== tVVmWa&

and kW10.5=+=+= 1.475.57total ga WWW &&& (breakingpower)

F

x

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251Afanistoacceleratequiescentairtoaspecifiedvelocityataspecifiedflowrate.Theminimumpowerthatmustbesuppliedtothefanistobedetermined.AssumptionsThefanoperatessteadily.Properties Thedensityofairisgiventobe=1.18kg/m3.AnalysisAfantransmitsthemechanicalenergyoftheshaft(shaftpower)tomechanicalenergyofair(kineticenergy).Foracontrolvolumethatenclosesthefan,theenergybalancecanbewrittenas

0/

energiesetc.potential,kinetic,internal,inchangeofRate

(steady)0system

massandwork,heat,bynsferenergy tranetofRate

==444 3444 2143421

&& dtdEEE outin outin EE && =

2ke

2out

airoutairinsh,

VmmW &&& ==

wherekg/s62.10/s)m)(9kg/m18.1(

33air === V&& m

Substituting,theminimumpowerinputrequiredisdeterminedtobeW340==

== J/s340

/sm1

J/kg1

2

m/s)8(kg/s).6210(

2 22

22out

airinsh,

VmW &&

DiscussionTheconservationofenergyprinciplerequirestheenergytobeconservedasitisconvertedfromoneformtoanother,anditdoesnotallowanyenergytobecreatedordestroyedduringaprocess.Inreality,thepowerrequiredwillbeconsiderablyhigherbecauseofthelossesassociatedwiththeconversionofmechanicalshaftenergytokineticenergyofair.2-76 A pump is pumping oil at a specified rate. The pressure rise of oil in the pump is measured, and the motor

efficiency is specified. The mechanical efficiency of the pump is to be determined.

Assumptions1Theflowissteadyandincompressible.2Theelevationdifferenceacrossthepumpis

negligible.PropertiesThedensityofoilisgiventobe=860kg/m3.AnalysisThenthetotalmechanicalenergyofafluidisthesumofthepotential,flow,andkineticenergies,andisexpressedperunitmassas 2/2mech VPvghe ++= .Todeterminethemechanicalefficiencyofthepump,weneedtoknowtheincreaseinthemechanicalenergyofthefluidasitflowsthroughthepump,whichis

+=

+==

2)(

2)(

2)()(

21

22

12

21

1

22

2inmech,outmech,fluidmech,

VVPP

VPv

VPvmeemE V&&&&

since vVV /&&& == m , and there is no change in the

potential energy of the fluid. Also,

m/s9.194/m)(0.08

/sm1.0

4/2

3

211

1 ====DA

VVV &&

m/s84.84/m)(0.12

/sm1.0

4/2

3

222

2 ====DA

VVV &&

PUMP

Pumpinlet

35kW

Motor

2

1

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Substituting, the useful pumping power is determined to be

kW3.26

m/skN1

kW1

m/skg1000

kN1

2

m/s)(19.9)m/s84.8()kg/m860(kN/m400/s)m(0.1

2

22323

fluidmech,upump,

=

+=

= EW &&

Then the shaft power and the mechanical efficiency of the pump become

kW5.31kW)35)(90.0(electricmotorshaftpump, === WW &&

83.6%==== 836.0kW31.5

kW3.26

shaftpump,

upump,

pumpW

W

&

&

Discussion The overall efficiency of this pump/motor unit is the product of the mechanical and motor efficiencies,

which is 0.90.836 = 0.75.

283CCarbondioxide(CO2),watervapor,andtraceamountsofsomeothergasessuchasmethaneandnitrogenoxidesactlikeablanketandkeeptheearthwarmatnightbyblockingtheheatradiatedfromtheearth.Thisisknownasthegreenhouseeffect.Thegreenhouseeffectmakeslifeonearthpossiblebykeepingtheearthwarm.Butexcessiveamountsofthesegasesdisturbthedelicatebalancebytrappingtoomuchenergy,whichcausestheaveragetemperatureoftheearthtoriseandtheclimateatsomelocalitiestochange.Theseundesirableconsequencesofthegreenhouseeffectarereferredtoasglobalwarming or global climate change. The greenhouse effect can be reduced by reducing the netproduction of CO2 by consuming less energy (for example, by buying energy efficient cars andappliances)andplantingtrees.