Summarization of Chapter 1 大 Continuum连续介质 Some Properties of fluids(流体的性质) viscosity(粘性 Definition(定义) The nature of viscosity(物理 Newtonian law of viscosity(牛顿内摩擦定律)
Summarization of Chapter 1 * Continuum 连续介质 * Some Properties of fluids(流体的性质) viscosity(粘性) Definition (定义) The nature of viscosity ( 物 理 ) Newtonian law of viscosity (牛顿内摩擦定律)
two different points of view in analyzing problems in mechanics The Eulerian view(欧拉观点 and the lagrangian view(拉格朗日观点) flow classification Stream line(流线) Pathline(迹线)& Flowfield 〔流场)流线方程,计算流谱 Surface force(表面力) and body force(质量力,体积力)
* Two different points of view in analyzing problems in mechanics The Eulerian view (欧拉观点)and the Lagrangian view （拉格朗日观点） * Flow classification * Streamline(流线),Pathline(迹线) & Flowfield (流场) 流线方程,计算流谱 * Surface force(表面力) and body force（质量力，体积力）
Summarization of Chapter 2 x Pressure Vertical to the surface and point into it At any point, pressure is independent of orientation * Equilibrium of a fluid element(流体静平衡) Vp= pR Equipressure surface(等压面) Pressure Distribution under Gravity(重力作用下的静压) Fluid in rigid body motion(加速运动流体平衡)
Summarization of Chapter 2 * Pressure Vertical to the surface and point into it. At any point, pressure is independent of orientation. * Equilibrium of a Fluid Element (流体静平衡) p R = Equipressure surface（等压面） Pressure Distribution under Gravity(重力作用下的静压) Fluid in rigid body motion(加速运动流体平衡)
Summarization of Chapter 3 Systems(体系) Control volumes(控制体) *RTT(雷诺输运定律) (D (pADout-cBoavin t 2 tt+d dp: any property of fluid(m, mv, H,e) dΦ dm The amount of p per unit mass Steady 1-d only in inlets and outlets
Summarization of Chapter 3 * Systems (体系) Control Volumes (控制体) * * RTT (雷诺输运定律 ) t+d t t+d t t t s ( ) ( ) s out in d AV AV dt = − : any property of fluid ( , , , ) m mV H E d dm = :The amount of per unit mass Steady , 1-D only in inlets and outlets
φ-mβ=dm/dm=1 ∑(nA1)m=∑(P,A1)m∑(m)m=(m)om Conservation of mass(质量守恒)( Continuity Equation) φ-mVβ=d(mV/dm=Ⅴ Fx= ri(v2x-vix) ∑ am m(out-v dt 2 2-out 1-in The Linear Momentum Equation(动量方程) Newton's Second Law Coordinate Control Volume
f=m =dm/dm=1 ( ) ( ) out in i i i i i i i i AV V = A ( ) ( ) i in i out i i m m = Conservation of mass (质量守恒) (Continuity Equation) f=mV =d(mV)/dm=V ) ( ) ( s out in d mV F m V V dt = = − 2－out, 1－ in F m V V x x x = − ( ) 2 1 F m V V y y y = − ( ) 2 1 F m V V z z z = − ( ) 2 1 o x y z The Linear Momentum Equation (动量方程) （ Newton’s Second Law ） * Coordinate , Control Volume
d=H=(rXv)m(Angular-Momentum)B dg F×1 ∑M=m(v20r2-0n1) The Angular-Momentum Equation p+ dp +gdz+dI V=0 p+dp V+d ++g21 P2+2+822 A+dA p+dp Frictionless incompressible Bernoulli equation k Streamline [ -2 section
d r v dm = = H r v m z ( ) (Angular-Momentum) = = The Angular-Momentum Equation ds Al + d A+ dA V + dV p + dp 2 dp p + p V A z + gdz +VdV = 0 dp g z c p V g z p V + + = + + 2 = 2 2 2 1 2 1 1 2 2 ( ) M m v2 r2 v1 r1 z = − • Frictionless incompressible Bernoulli Equation * Streamline, !-2 section
dE d=E, B e m First Laws of Thermodynamics de do dw d-M (V2-V12)+g(二2-=1)+(h2-h1) The energy equation per unit mass
, dE E e dm = = = The energy equation per unit mass 2 2 2 1 2 1 2 1 1 ( ) ( ) ( ) 2 s q w V V g z z h h − = − + − + − First Laws of Thermodynamics dE dQ dW dt dt dt = −
Summarization of chapter 4 The Acceleration Field of a fluid(加速度) (.V Nonlinear terms Local acceleration Convective acceleration a ≠0 unsteady ≠0 nonuniform dt d a Substantial material derivative +(VV) Dt at 随体(物质、全)导数
Summarization of Chapter 4 • The Acceleration Field of a Fluid(加速度) V V t V a + ( ) = Local acceleration unsteady 0 t Convective acceleration nonuniform 0 i x Nonlinear terms ( ) D V Dt t = + Substantial (Material) derivative 随体（物质、全）导数
* Differentia| Equation of Mass Conservation(连续方程 +v(p)=0V(p)=0 t dttov. V=0 V·=0 Differential Equation of Linear Momentum(动量方程) 二维定常不可压
* Differential Equation of Mass Conservation(连续方程) ( ) 0 V t + = + V = 0 dt d = ( ) 0 V V = 0 •Differential Equation of Linear Momentum(动量方程) 二维定常不可压
F OX F=[()+()j+()]hxvo dz ax Ti =2uSi-ou(vv-Po dv R-VP+少2+(V·V) dt 3
F ma = 1 ( ) ji i i j du X dt x = + [( ) ( ) ( ) ] ix iz iy s i i i F i j k dxdydz x x x = + + 1 1 2 ( ) 3 dV R P V V dt = − + + 2 2 ( ) 3 ij ij ij ij = − − S V P