简介：Themechanicalenergyequationisafundamentalequationofa1-DmathematicalmodelinHydraulicsandEngineeringFluidMechanics.ThisequationforthetotalflowusedtobededucedbyextendingtheBernoulli’sequationfortheidealfluidinthestreamlinetoastreamtube,andthenrevisedbyconsideringtheviscouseffectandintegratedonthecrosssection.Thisderivationisnotrigorousandtheeffectofturbulenceisnotconsidered.Inthispaper,theenergyequationforthetotalflowisderivedbyusingtheNavier-StokesequationsinFluidMechanics,theresultsareasfollows:(1)Anewenergyequationforsteadychannelflowsofincompressiblehomogeneousliquidisobtained,whichincludesthevariationoftheturbulentkineticenergyalongthechannel,theformulaforthemechanicalenergylossofthetotalflowcanbedetermineddirectlyinthedeductionprocess.(2)Thetheoreticalsolutionofthevelocityfieldforlaminarflowsinarectangularopenchannelisobtainedandthemechanicalenergylossintheenergyequationiscalculated.ThevariationsofthecoefficientofthemechanicalenergylossagainsttheReynoldsnumberandthewidth-depthratioareobtained.(3)Theturbulentflowinarectangularopenchannelissimulatedusing3-DReynoldsaveragedequationsclosedbytheReynoldsstressmodel(RSM),andthevariationsofthecoefficientofthemechanicalenergylossagainsttheReynoldsnumberandthewidth-depthratioarediscussed.

简介：Thedynamicsofliquidsloshinginasphericaltankwithspacerunderlowgravitywasinvestigated.Byextendingthecharacteristicfunctions,thefrequenciesofliquidfree-sloshing,reactionforceandmomentsonthewalloftankwereobtained.Bymechanicalequivalentprinciple,theequivalentmodelsofspring-vibrator-damperofliquidsloshingweregiven.Thenumericalresultsobtainedshowwhenaspacerisinsertedinthetank,thesloshingfrequencyofliquidandthesloshingmassofliquidwilldecrease.