第4課基本原理和基本方程-數(shù)學(xué)基礎(chǔ)

空氣動(dòng)力Less.4矢量關(guān)系回 re ortant,the

用的概流函速度實(shí)際空氣動(dòng)問(wèn)題的Less.4SomeLess.4SomeFundamentalPrinciplesandSomevectorLess.4Less.4SomeFundamentalPrinciplesandLess.4Less.4SomeFundamentalPrinciplesandScalarandvectorfields標(biāo)（數(shù)）量場(chǎng)和iAiABjBy iAyBzAzByj(AzBxAxBz)k(AxByAyBxkLess.4SomeFundamentalPrinciplesandScalarandvectorproducts數(shù)量積和矢量Less.4SomeLess.4SomeFundamentalPrinciplesandGradientofascalarfield壓力等值Less.4Less.4SomeFundamentalPrinciplesandGradientofascalarfieldiscalleddirectionalderivativeinthesS方向的方向Less.4Less.4SomeFundamentalPrinciplesandGradientofascalarfieldLess.4Less.4SomeFundamentalPrinciplesandDivergenceofavectorfieldThetimerateofchangeofthevolumeofamovingfluidelementoffixedmass,perunitvolumeoftha ement,isequaltothedivergenceofV,denotedby▽·VLess.4Less.4SomeFundamentalPrinciplesandCurlofavectorfieldAngularvelocityωisequaltoone-halfofthecurlofV,▽×Less.4Less.4SomeFundamentalPrinciplesandLineintegrals線積ALess.4Less.4SomeFundamentalPrinciplesandSurfaceintegrals面積Thethree-dimensionalsurfaceareaSisboundedbytheclosedcurveCLess.4Less.4SomeFundamentalPrinciplesandLess.4Less.4SomeFundamentalPrinciplesandRelationsbetweenline,surface,volume定散度梯度Less.4Less.4SomeFundamentalPrinciplesandModelsofthefluid:controlvolumesandfluidThereisacertainphilosophicalprocedureinvolvedwiththedevelopmentoftheseequations,asfollows;Invokethreefundamentalphysicalprinciplesthataredeeplyentrenchedinourmacroscopicobservationsofnature,namely,Massisconserved(i.e.masscanbeneithercreatednorNewton’ssecondlaw:force=massEnergyisconserved;itcanonlychangefromoneformtoDetermineasuitablemodelofthefluid.Rememberthatafluidisasquishysubstance,andthereforeitisusuallymoredifficulttodescribethanawell-definedsolidbody.Hence,wehavetoadoptareasonablemodelofthefluidtowhichwecanapplythefundamentalprinciplesstatedinterm1.Less.4Less.4SomeFundamentalPrinciplesandModelsofthefluid:controlvolumesandfluidThereisacertainphilosophicalprocedureinvolvedwiththedevelopmentoftheseequations,asfollows;Applythefundamentalphysicalprincipleslistedinterm1tothemodelofthefluiddeterminedinterm2inordertoobtainmathematicalequationswhichproperlydescribethephysicsoftheflow.Inturn,usethesefundamentalequationsto yzeanyparticularaerodynamicflowproblemofinterest.Less.4Less.4SomeFundamentalPrinciplesandModelsofthefluid:controlvolumesandfluidFinitecontrolvolumeapproachInfinitesimalfluidelementapproachMolecularapproachLess.4Less.4SomeFundamentalPrinciplesandPhysicalmeaningofthedivergenceofvelocity速度散度物L(fēng)ess.4Less.4SomeFund