寫作模版評點mcm各部分公式

WeassumelaminarflowanduseBernoulli’sequation:（由假設得到 Accordingtotheassumptionsateveryjunctionwehave（由于假設Becauseourfieldisflat,wehave ,sotheheightofoursourcerelativetooursprinklersdoesnotaffecttheexitspeedv2（由原因得到的 Sincethefluidis pressible(由于液體是不可壓縮的wehave Pluggingv1intotheequationforv2,weobtain（ 1代 2中得到Puttingthesetogether(把 放在一起),becauseofthelawofconservationofenergy,Therefore,from(2),(3),(5),wehavetheithjunction（由前幾 得Putting(1)-(5)together,wecanobtainpupateveryjunction.infact,atthelastjunction,wehavePuttingtheseinto(1),weget（把這些 代入1中）WhichmeansthatCommonly,hisFromtheseequations,（從這 中我們知道）weknowthatUsingpressureanddischargedatafromRainBird結(jié)果Wefindtheattenuationfactor（得到衰減因子，常數(shù)，系數(shù)）toTofindthenewpressure,weusethe(00),whichstatesthatthevolumeofwaterflowinginequalsthevolumeofwaterflowingout:（為了找到新值，我們用什么方程）()is;;SolvingforVNweobtain( Wherenisthe…..Wehavethefollowingdifferentialequationsforspeedsinthexandydirections:Whosesolutionsare（解）Weusethefollowinginitialconditions(使用初值todeterminethedragWeapplythelawofconservationofenergy（根據(jù)能量守恒定律）.TheworkdonebythesisThedecreaseinpotentialenergyis（勢能的減少Theincreaseinkineticenergyis動能的增加Drugactsdirectlyagainstvelocity,sotheaccelerationvectorfromdragcanbefoundNewton’slawF=maas:(第二定律)WhereaistheaccelerationvectorandmisUsingtheNewton’sSecondLaw,wehavethatF/m=aandSothatSettingthetwoexpressionsfort1/t2equalandcross-multiplyingWeapproximatethebinomialdistributionofcontenderswithanormalWherexisthecumulativedistributionfunctionofthestandardnormaldistribution.ClearingdenominatorsandsolvingtheresultingquadraticinBgivesAsanyticapproximationto.fork=1,wegetB=c26．Integrating,（使結(jié)合）wegetPVT=constant,whereThemaincompositionoftheairisnitrogenandoxygen,soi=5andr=1.4,AccordingtoFirstLawofThermodynamics,wegetWhere( ).wealsothenhaveWherePisthepressureofthegasandVisthevolume.WeputthemintotheIdealGasInternal DefineA=nlwtobethe )（定義）;rearranging(1)produces（ WeizeEforeachlayer,subjecttotheconstraint(2).Thecalculationsareeasierifweminimize1/E.（為了得到最大值，求他倒數(shù)的最小值）Neglectingconstantfactors（忽略常數(shù)）,weminimizeSubjecttotheconstraint（使服從約束條件WhereBisconstantdefinedin(2).However,aslongasweareobeyingthisconstraint,wecanwrite（根據(jù)約束條件我們得到）Andthusfdependsonlyonhthefunctionfisminimizedat（求最小值Atthisvalueofh,theconstraintreducesThisimplies（暗示）thattheharmonicmeanoflandwshouldSo,intheoptimalsituation.Thisvalueshowsverylittlelossduetofriction.（結(jié)果說明）TheescapespeedwithfrictionWeuseasimilarprocesstofindthepositionofthedroplet,resultinginWitht=0.0001s,errorfromtheapproximationisvirtuallyzero.Wecalculateditstrajectory(軌道Forthatcase,usingthesameexpansionforeasSolvingfortandequatingittotheearlierexpressionfort,weRecallingthatinthisequalityonlynisafunctionoff,wesubstitutefornandsolveforf.theresultisAsv=…,this essingular(單數(shù)的TherevenuegeneratedbytheflightThenweWedifferentiatetheideal-gasstateequationWeeliminatedTfromthelasttwoequationstoget（排除因素得到Wefistexaminethepath