流体力学基本方程

1、流体力学基本方程：基本定律质量守恒定律备注输运定律F(xrf)c/V=十fF(rf)b*nJ4.高斯公式川可!/=li-QeMvA物质导数DFdf”Dtdt积分形式拉氏描述石1p(x,t)dV=0.V(t/p；仍卩+/P(x,f)u(x,t)*ndA0Vt)皿)使用输运定律欧拉描述春/卩仇fM卩+/f2U)W0U)切如A=0.连续性方程J瞅:；V+广捡啊训:ncW=J+叫户匡蚀芯”)旳=0旳柏VU；-+V*(p(xrf)u(xzf)=0拉氏描述下的质量守恒定律运用咼斯公式EdM+WuD引入物质导数分量形式dp)6(/7化)d(pu_)dtdxdydz柱坐标引川巩卩心3/pwja+為十赧十玄一球

2、坐标定常V-(p(x,f)u(xz/)=0.詁-0St不可压V*u(xzt)=0p=常矍流线迹线引入势函数基本定律输运定律高斯公式物质导数动量守恒定律欧拉描述拉氏描述积分形式/bM）1财曲）-伽期仙）*。鳖叫）+箱（叫旳）=陶+碁述下质量守恒定律运用高斯公式Duj。f、临T_他+曲（可引物质数本构方程Thestressinamovingfluid吋p+Sj（T寸2/xSij+XSmmdjpS平科刖7u=ij=一Pij+2/lSy+XSmmV3砌+（3+入）Vu.卩=尹引速度的系p-p=+Wu不可压P如+2心/如+2Q3stokesassumption；+lWithoutusingTij=-卩列

3、+2“(Sij-+RiSwmStokesassumption12二(di-+(2di(2dxy),=-p+2fil叽)+l-討dumN-Sdu；dpdxj-dxPS/1/.地、dxjJ/2方程1UUrpdt+吗j+场“叫_LdXi+（如-于Cigr1丿亦珂1柱面坐标系（积F分量岛+卩冷;呀:红）診普ar13,.1i带叫2dvsivrs分H卩（芮f和+厂刑厂+%丿伽r391r1f.1,1”%,2氏护础3rr卅心r29护r1&3z22分.H警乜警+严务+%务）w-替1方/肌上17%川丨“小厂（升r丿新汁卅i可压D丐即护吟（1ddum.%=一鬲+喝+嚼+（血埒丿隅厲np贬）不可压p冒-Vp+pg+a

4、iV2u(incompressible)不可压Whenthefluiddensityisconstant棉=-V+mV2u.卩f二pPsf无粘丽=-Yp+PgdH/dt=Mf角动量定理(rxpudViJv雷(rxptL)dV+/(rxpuJfu-nJdA,A(i)(rxpu)dV十/(rxp)dV+/(rxf)dAf讥0A(t)I(rxpu)(u*n)rf/l8f(rxpu)t/V十/(txpu)(un)cL4基本定律能量守恒定律备注输运定律：纟/F(xrf)cJV=/越+fndA.咼斯公式ff/v=/QdAvA物质导数DFdF尸_U.VF积分形式拉氏描述壬护(於1；同)川讨=f*边讨11fu

5、沖貝一/q*ndArVt)v(t)AltMJ鲁(+f(八+|u|2)(tin)cM=JgudV+j(9udAjqiuM(f)4(?)V(f)A(f)A(f)使用输运定律非惯性坐标系欧拉描述疋+扣j(x+o|a)(ub)nM冲!pg-urfV亠/fUiAyq-rA,ajUJAio/如拉氏描述下质量守恒定律运用咼斯公式引入物质导数DeDv11dqiDt=PDt+7ijijPiBernoullisequation:derivedfromtheN-Smomentumequationandtheenergyequationundervarioussetsofconditionsenergy:N-S:：o

6、btainfromN-Sequation1:inviscidflow、），n-SequationchangetoEulerequationditjduj1dpddf+UldXpdxjdXjIftheflowisalsobarotropic7thenpp（p）Constantdensity（常密度）,isothermal（绝热），andisentropic（等熵）flowsarebarotropic（正压）B=steadyflow(duj/dt0)4：theflowisirrotational3：unsteady，irrotational1：obtainfromenergyequationste

7、adyflow(d/dt=0)(呵qi=0)2：Intheabsenceofviscousstressesandheattransfera(puf)/3x；=3：constant-viscosity，constant-density，irrotationalflow，incompressiblePconstantg=V(gz)zandw04：constant-viscosity，constant-density，irrotationalflow罟+扣eF+gz+彳=constant.TheBoussinesqApproximationTheBoussinesqapproximationappliesiftheMachnumberoftheflowissmall,propagationofsoundorshockwavesisnotconsidered,theverticalscaleoftheflowisnottoolarge,andthetemperaturedifferencesinth