写作模版评点mcm各部分公式

WeassumelaminarflowanduseBernoulli’sequation:（由假设得到 Accordingtotheassumptionsateveryjunctionwehave（由于假设Becauseourfieldisflat,wehave ,sotheheightofoursourcerelativetooursprinklersdoesnotaffecttheexitspeedv2（由原因得到的 Sincethefluidis pressible(由于液体是不可压缩的wehave Pluggingv1intotheequationforv2,weobtain（ 1代 2中得到Puttingthesetogether(把 放在一起),becauseofthelawofconservationofenergy,Therefore,from(2),(3),(5),wehavetheithjunction（由前几 得Putting(1)-(5)together,wecanobtainpupateveryjunction.infact,atthelastjunction,wehavePuttingtheseinto(1),weget（把这些 代入1中）WhichmeansthatCommonly,hisFromtheseequations,（从这 中我们知道）weknowthatUsingpressureanddischargedatafromRainBird结果Wefindtheattenuationfactor（得到衰减因子，常数，系数）toTofindthenewpressure,weusethe(00),whichstatesthatthevolumeofwaterflowinginequalsthevolumeofwaterflowingout:（为了找到新值，我们用什么方程）()is;;SolvingforVNweobtain( Wherenisthe…..Wehavethefollowingdifferentialequationsforspeedsinthexandydirections:Whosesolutionsare（解）Weusethefollowinginitialconditions(使用初值todeterminethedragWeapplythelawofconservationofenergy（根据能量守恒定律）.TheworkdonebythesisThedecreaseinpotentialenergyis（势能的减少Theincreaseinkineticenergyis动能的增加Drugactsdirectlyagainstvelocity,sotheaccelerationvectorfromdragcanbefoundNewton’slawF=maas:(第二定律)WhereaistheaccelerationvectorandmisUsingtheNewton’sSecondLaw,wehavethatF/m=aandSothatSettingthetwoexpressionsfort1/t2equalandcross-multiplyingWeapproximatethebinomialdistributionofcontenderswithanormalWherexisthecumulativedistributionfunctionofthestandardnormaldistribution.ClearingdenominatorsandsolvingtheresultingquadraticinBgivesAsanyticapproximationto.fork=1,wegetB=c26．Integrating,（使结合）wegetPVT=constant,whereThemaincompositionoftheairisnitrogenandoxygen,soi=5andr=1.4,AccordingtoFirstLawofThermodynamics,wegetWhere( ).wealsothenhaveWherePisthepressureofthegasandVisthevolume.WeputthemintotheIdealGasInternal DefineA=nlwtobethe )（定义）;rearranging(1)produces（ WeizeEforeachlayer,subjecttotheconstraint(2).Thecalculationsareeasierifweminimize1/E.（为了得到最大值，求他倒数的最小值）Neglectingconstantfactors（忽略常数）,weminimizeSubjecttotheconstraint（使服从约束条件WhereBisconstantdefinedin(2).However,aslongasweareobeyingthisconstraint,wecanwrite（根据约束条件我们得到）Andthusfdependsonlyonhthefunctionfisminimizedat（求最小值Atthisvalueofh,theconstraintreducesThisimplies（暗示）thattheharmonicmeanoflandwshouldSo,intheoptimalsituation.Thisvalueshowsverylittlelossduetofriction.（结果说明）TheescapespeedwithfrictionWeuseasimilarprocesstofindthepositionofthedroplet,resultinginWitht=0.0001s,errorfromtheapproximationisvirtuallyzero.Wecalculateditstrajectory(轨道Forthatcase,usingthesameexpansionforeasSolvingfortandequatingittotheearlierexpressionfort,weRecallingthatinthisequalityonlynisafunctionoff,wesubstitutefornandsolveforf.theresultisAsv=…,this essingular(单数的TherevenuegeneratedbytheflightThenweWedifferentiatetheideal-gasstateequationWeeliminatedTfromthelasttwoequationstoget（排除因素得到Wefistexaminethepath