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
* 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
* 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 )
Rp ????
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 )
t+d
tt+dt
tt
s
( ) ( )s o u t in
d A V A V
dt ? ? ? ?
? ??
?, any property of fluid (,,,)m mV H Err
d
dm?
??,The amount of per unit mass ?
Steady,1-D only in inlets and outlets
f=m ??dm/dm=1
( ) ( )o u t i niiii ii
ii
A VV A? ???? ( ) ( )i in i o u t
ii
mm???&&
Conservation of mass (质量守恒 ) (Continuity Equation)
f=mV ??d(mV)/dm=V
)
() (s
o u t in
d m VF m V V
dt? ? ??
rr vv
&
2－ out,1－ in
21()x x xF m V V??&
21()y y yF m V V??&
21()z z zF m V V??&?
o x
y
z
The Linear Momentum Equation (动量方程 )
（ Newton’s Second Law ）
* Coordinate,Control Volume
d rv
dm?
?? ? ?vv()zH r v m? ? ? ?v vv (Angular-Momentum)
The Angular-Momentum Equation
ds
Al
?? d?
dAA?
dVV?
dpp?
2dpp?
?
?
p
V
A
?
z
0??? V d Vgdzdp?
czgVpzgVp ?????? 2
2
22
1
2
11
22 ??
)( 1122 rvrvmM z ?? ??? ?
Frictionless incompressible
Bernoulli Equation
* Streamline,!-2 section
,dEEedm?? ? ? ?
The energy equation per unit mass
22
2 1 2 1 2 1
1 ( ) ( ) ( )
2sq w V V g z z h h? ? ? ? ? ? ?
First Laws of Thermodynamics
d E d Q d W
d t d t d t??
Summarization of Chapter 4
? The Acceleration Field of a Fluid(加速度 )
VVtVa ??
??
)( ??????
Local acceleration
unsteady 0
t
? ?
?
Convective acceleration
nonuniform 0
ix
? ?
?
Nonlinear terms
()D VD t t?? ? ??? r
Substantial (Material) derivative
随体（物质、全）导数
* Differential Equation of Mass Conservation(连续方程 )
( ) 0Vt? ?? ? ? ? ?? v
0???? Vdtd ???
( ) 0V?? ? ?v
0??? V?
?Differential Equation of Linear Momentum(动量方程 )
二维定常不可压
F ma? 1 () jii
i
j
du X
d t x
?
?
?
??
?
[ ( ) ( ) ( ) ]iyi x i zs
i i i
F i j k d x d y d zx x x??? ???? ? ?? ? ?
vvv
211 ()
3
dV R P V V
dt
??
?
? ? ? ? ? ? ? ? ?
v v v v
22 ( )
3i j i j i j i jS V P? ? ? ? ?? ? ? ? ?
v
*The Differential Equation of Energy
.,d E d e
Q W d x d y d zd t d t ?? ? ?
.
()jij
i i i
u T q
x x x? ? ?
? ??? ? ?
? ? ?
?du
dt?
单位
体积
内能
变化
率
热传导
等传热
变型时
表面应
力做功
.
()
ii
D s TTq
D t x x? ? ?
??? ? ? ?
??
.()
ii
D h D P T q
D t D t x x? ? ?
??? ? ? ? ?
??
.
()
ii
D T TC v P V q
D t x x? ? ?
??? ? ? ? ? ? ? ?
??
v
.
()
ii
D T D P TC p q
D t D t x x? ? ?
??? ? ? ? ?
??
已知 D? = CvDT,Dh = CpDT
* Exact Solution of N-S Equations
Couette Flow,incompressible,steady,laminarflow
between a Fixed and a Moving Plate neglecting
body force
h
h
x
y
o
V
0,0,0u v wz? ? ? ? ??
* Dynamical Similarity and Nondimensionalization of N-
S Equation
Re 雷诺数
Summarization of Chapter 5
* Three Thicknesses of a Boundary Layer
BL Thickness (名义厚度，厚度 ）
Displacement Thickness (排移厚度 ）
Momentum Thickness (动量厚度，动量损失厚度 ）
* Momentum Integral Relation for Flat-plate BL
2
w
dU
dx
???? 2u a by c y? ? ?
* Boundary Layer Equation Blasius 1908
* Assumptions for compressible flow
Summarization of Chapter 6
*Bernoulli equation for compressible flow
*The speed of sound
*Shock Wave