ページ3:

© α = ?
ideal fluid KE
Weight
•real fluid KE
dm pudAde
d (KE)
=
Weight
=
α
mu
y
三速度水頭
mg
一小塊流體
+ (dm) u² = ± pu³ dAdt
=
J KE & hi * - Pu³ JA
動能流率= +
dt
x
SJA us da
A V³.
無因次
© p. ?
Se [ U. (1-1)] B.dy
-R
16
ideal fluid Momentum
real fluid
B
=
Sheuda
*0% (VA
t
Momentum
S
=
(BR)()户
-R
=
eQu
12.3
dj
-1.54
Beau = & SendA
fr [uc (1-1-1-1)] * B dy
(+BR) (3 uc)²
=1.2

ページ4:

Renolds Decomposition
u = ū - u'
u = instaneous velocity D
=
u time average velocity. Soudt.
時間平均速度
777ot
n' = velocity fluctuation (3)
u
13
© 4' = ?
time
4 = 0
U'u'
=
>
(u')² =
(W)
20
5- turbulent intensity
紊流强度

ページ5:

{
u = const.
=>
ū # const =
Steady
unsteady
'u'v' tt'* ED P 12 J
u'水平方向跳動
垂直方向跳動
B
A
C.V.
Ao
uth
B
V'
v可能也可能↓
A
For B
IQ Vont -in)
Σ Fx = -TA₁ = ( ( V'A.). [-(-4)]
0
-Chev A. u'
剪力方向(x)
=
evAou'
=
ev'n'
R
Renolds shear stress

ページ6:

@
Newton's
Ju
dy
分子粘滞性
molecular viscosity
wwwwww
7 turbulence = CN + Zp=
ε Eddy viscosity.
真實流體不會只是一條線
會有跳動
dū
dy
M.
dy
-er
涓動黏滯性
簡化
① 層流 vs.紊流
Laninear
Newton Reynolds
(M+E).
Turbulent
dū
dy

ページ7:

EX 2. ME for BE
U
U
7.平均摩擦剪應力
71
一个个个个个↑
C.V.
D CE
dmsys
dt
=
± duly 10
T
.0.
=
Steady
It fff est
se
C.V.
out
+
a.S.
Th
and - m + up & ds=
0
=
f
·S
e
e
YUB Jy +m- eU (SB)
£
e (UB) s² + m - P U S B
m = PUSB =—=— PUSB
-
2
= = USB

ページ8:

79
- Z. (LB) = - — " e BU'S
T₁ ='
ev's
8.0927-
(87)°2-43
=
· Seu (Body)
Pu (Bdy) u + MU - PU(BS)
-LBU" So y³dy + (PUSB) - evBS
"BU² 8³
3
Pand-
ME

ページ9:

Navier-Stoke
equ.
真實流體方程式
向量式
17 ½ + ( p +eg +
e
1th ho
-up + eg + m² + 44 (0)
pressure gravity. Visocity compresibility
Steady flow
force
20
dt
= D
forceforce
Ideal fluid Incomprensible
M = 0
Ju
+x
Ju
t
dy
T
= 0
2
a
op-eg
=
層流
give yo
eg 流體靜力學基本方程式
Assumptions
▽(nabla)的定義
所以它是一個由偏微分組成的向量。
♦ ∇ ·V是什麼?(散度 divergence)
Du De One
@ Imcompensible fluid
②
·√
Steady flow
= 0
+2=0
ot
③ D parallel flow
u+ D
V=W = 0
Infinitely wide au
④
板子。
dz
= 0

ページ10:

D. CE
Ju JV/
xe
+
We
0
+
0
MP
=
0 =>
xe
y=0, u+ f(x)
@ N-5 (x-dir)
Vie
nt
ne
u
34-0 u= f (z)
ze
ne
=
'
de
[ u = fly)
ju tu du + vay + w dy = +34 +94 +4 (34 34.3%)
ot
N-S (y-dir)
xe
nt
de
ry
de
xe
+ v
ne
+W.
dz
ñe
20
=
V=D.
-eg P = -egy + f(x)
JP = f'(x) of = fly)
=
=
xe
号(醬):(古
dy
再積
岢)
xe w
+
x
ex
zhe
g+(紫++)
g
純入函收
積分
du
),位器+
>> n ( y ) = (+1 3+ ) y² + C₁Y + Cz
xe
·CC Bo's RR.
boundary condition
y C₁
V=D

ページ11:

Ex1. Couette flow上板移動
BC2
y=a
y=a, u = U
V
u = U
條件: 背=0(不受雁)
MV
7 =
a
y=o
y
U= 0
fixed
BC1
71372
BC1: C2=0
=
+
·ulys - 1 C₁y + 00
Bcz: C. a. U c..
'
uly) Ly
du
dy
=
a
M
a
=
const.
·庫維特流 Couette:由邊界的運動(例如:上板移動)產生的流動。
·帕數葉流 Poiseuille:由壓力差(入口高壓→出口低壓)產生的流動。

ページ12:

EX 2 Poiseuille flow
Pk
BC2
y=au=0 1554
9
PN.
1=0
BC1
y= o, u=0
1100
z‹y)
條件: 裴0(受厠)
why
Umx - (132) a² u(y) = (1/3) y ² + C₁y + Cz
BC 1 C₂ = 0
:
0 = (++1 344) a² + C₁a
BC 2 0 =
C₁ =
-
(ISP) a
uly ) = ( ^ &x) (y²- ay)
U 12 16 3
u極值時, dy
= 0
=
:
,
zy-a. o. y. a
,
U Max ( 1 ) ( (2)² - a ( 2 )) = -a (37)
M.
(j) = Mdy = (+ x) (zy-a)
=
(+) (³y-a)

ページ13:

EX. 3 Given I assumptions
。 inf wide by :0
Steady flow &
=
+t
= 0
Paralle flow w#O
u = V = 0
@ incompensible (..) en
=
BC1
•W=0
Z
p = 0
vg
BC2
x-h
air
7=0
求流速分布
9z = -9
①((x = h ) = 0. (Air-oil 7 J₁s, %).
i compensible
b.剪應力分布
JW
= 0
Jz
84
t
=0
→ W= f(x)
= 0
ry
(
=
+MD++(3)
-Peg +
pressure gravity Visory compresibility
force
force force:
Incompensible
N-S x-dir
+ W
Ju
dx
+
-JP/
+
=
+
+
+
x
0 = 0

ページ14:

N-Sy-dir 0=0
N-S 2-dir
MP
MP
xe
-JP
-eg.
1
(( x + y) dt + ( x )
+ li
+
=
0 =
- eg + μ
+
M
Me
+
+
JW²
eg
dx²
M
BC1
Me
8×
=
eg
W
= x + C ₁.
w (x) = eg x² + C₁ X + Cz
X=0, W = 0 → C₂ = 0
BC2 x = h, 2=0 = μdx.
0
=
Wz
→ x=h,
when x- h, dw=0
egh + Ci
M
w(x) = 19 x 19 x
egh
M
=
,
話(x²:zhx)=次抛物線
w by 1 3 1 1 1 2 4 2 d W = 0
W Max
Ci
2x-21=0x-h
= (12) (h²->h³) = (1/2) (- h³)
=
-egh

ページ15:

71x)
=
M
d (eg (x²-2hx))
dx
12 (2x-2h) = eg(x-h)
2.
一次線性

ページ16:

EX. 4
-gous as
V
A
995
=g sing
Bc1
h=0
x
+
US:- VPN\
11.
先假設16:0
(fixed Assumptions
Bc2
n=h
US-0
·(s;y,n)
· (us, Viun)
CE (V不進出)
•pensible
incom
Jus
+
<
• incompensible fluid (vo)
2
steady flow $0.
= 0
• ID paralle flow (USTO
• inf wide dy = 0
=> Us = f (n)
{
V = Un = 0.
Jus
=0
Jun
dy
= 0
Jn
Jus
= 0
N-S s-dir
Jus
+
+
ry
us
((du udus vous vous) --dr + lgs + u dus dins d'us)
=
t
Jus
ryz
+
JS
0
=
-JP + egs +μ.
Jus
8h2
= ( 3 - (95)
us (n) (= ^^) ($5 - egs) n² + c.n + c₂
|

ページ17:

BC 1 n = 0, US - - V, C₂ = - V
Bc 2 n=h₁ u₂ = 0 =
V
( 2 ) ( 3/5 - egs) h² + C₁h-v
C₁ = ( = 14) (de - egs) h +
V.
h
Us (n) = ( = ^) ( +15 - egs) (n³ - hn) + v(^^ -1)
線性 Us(n)=√(1-1)
110 1 tk
拋物線
(^) (& egs) (n°-hn)
US $ 3 1 3 2 42 Jus
an
-
= 0 zn - h = 0; n =
Us Max = (1/1) (3 pgs ) ( ½ ½)
-
-
N-Sy-dir
0=0
N-Sn-dir
Jun
((dan + udum voln
Jun
=
-JP
dn
+
of egn
=
(gn
+
I Jun Jun Jun
+
+
th

ページ18:

u
=
P(s, n) - P. + (dt)s egn n
= Po + (3) segasα
+
d
u (+1) + s(31) = (o'old- (us) d
Je
Se
de
定義:
ZA Jp = π ds + de dy
· P(sin)
=
Se
ay
+
up ye
de
dp fds + sf dy + JP dn

ページ19:

Given α =
65°
h = 4mm
9:750 51
V
=
=
M
0.5
m
: 1000
cm
S
=
when n-h, dus
V
h
提供多少??
+
"
0
m
S.
0.5
100
0
m
5
為了使油液不下滑
妮20的min=?
> 0 67 min = ?
us (n) = ( 2 ) ( de 5 pgs) (n²-hn) + v(^-1)
dus (= m)
dn
n=h
=
z
-
(31/3 pgs) (2n-h) +
V
h ( x n ) ( de egs) + + = 0
(de egs) + 2MV = 0
Jp
ds
-
=
h²
egs - Av
h²
6200(二)

ページ20:

Steady Laminar velocity profile.
in
O
Σ√x = 0
dx
O
力平衡
<r+dr
Px
Px+dx
Tr
=
- Px (2πr dr) - Px +dx (2πr dr) + (Z: 2πordx) - (7·2πr dx) redr
(2Tkr dr) (Px- Pr+dx) + (2tudy) [(rz)r - (87)r+ar ] = 0
PxPx+dx
-
dx
dr ax
1P+1(21) -^(21)
lim - dp
dx70
dro
=
(21)P
dr
=0
2
of r + d (μrou)
dp
of = (17) or (du)
dr
=
-
- 1x
= 0

ページ21:

P*
刚取国管,现在取固桶
xp1
M2.
Zw
|
·Px+dx
Pri
ΣFx = Px (TUR²³) - Px+dx (TUR) - Zw (2TVR √x)
lim
a = "22 + d(-1) ==
0 Exp
積到
"
dx
const.
=
(R) Z w <O
特刊 (1) rdr=d(r)
(六)(x)+C=Y
du
= Y Jr
:Y(六)(米)+/
=
[[(六)(x)+] = du
dr
TRY (+1) (d); + Color + C₁ = u(r)

ページ22:

( + h ) ( t ) ;² + C₁ lnr + C₁ = u(r)
BC 1 r = 0
Ju
dx
=
D
O + C₁ ∞ = 0 ; C₁ = 0
BC 2 r = R
1=0
(+/+) (+) R² + C₁ = 0
C₁ = - (++) (+) R²
2
(u(r) = (++) (+) - (++) (+) R²
= (++) (+) (r-R³)

ページ23:

pipe flow 管流
滿管 P. wg
²
Z₁ t
+x
29
。
Laminar
工主要f
head loss < 1.次要配件
hi
Zz 21+2+
|Turbulent
乙大
Entry length 入口長度
D
小
|-
紊流入口長度短→動量傳遞旺盛
Turbulent lager
Overlap layer 過度層
Buffer layer 緩衝層
Viscous layer 黏滞次居
(Cominar sublayer 層流次居)
turbulent
viscous
黏滞性

ページ24:

1. Majar head loss
L. Pipe length
管長
hf f 1 y
摩擦水頭損失
·f⋅f (e, U. D. v) = f (e, vb)
D: Pipe diameter A
e Roughness height
粗糙度
f
Moody Chart (慕迪圖)
Re79
•R•
Re
VD
D
4182f
15頁,共10頁
1. Minor Head loss h₁ = key.
I
entrance
he = key
@ exit hx = kxxy
Ⓒ contraction h
=
Re
ke:水頭損失係數
④
expansion
突捩he
(V₁-V)
=
2g
k₁ = 1
bend Bhb

ページ25:

EX. Part 1
EL
0.5
29.
:
靜止oh
Zik=0.48
m
HGL
f
0.2
Given D= 0.1 m
水管直径D=0.1m
V = 1.5
= 1.5m
AD ke = 0.5
valve 閥門ku
-U = 0.2
出口k x = 1.0
if→ Moody diagram
Re = VD
e
b
=
✓
10-6
71412-
V同定
L = 10m
,
e
=
2x10m
粗糙度
1.106 m²
2 =
S
72
0 h = ?
=
靜止
Datum (7-0)
=>
②
EL.HGL
Moody Diagram
0.1.
0.09
0.08
Region
0.07
10.05
0.06
10.04
10.03
0.05%
10.02
0.040
10.015
10.01
0.03-
0.005
0.1
-= 0.002
0.025-
0.002
0.02.
0.001
5x10-4
0.015
2x10-
Complete
10-4
0.01
5x10
ALIA
2× 10-4
Relative Pipe Roughness 5
f = 0.025
岢
• N. + *
=
Z₁
x
=
|
• 20
H₂ = PL
岢
Z2
ENGINEEREXCEL
10%
104
10%
Reynolds Number, Re = pd
0-5
5x10-6
Smooth Pipe
10-
107
100

ページ26:

H₁ - kevy -kuv - kxy - fb v
-key-buy-by-phy - He
次要
主要
29.
=
(2₁-22) - (ke+ku+kx + fr ) ( ) = 0
0h-(05+02+10+25) (2151) = 0
oh = 0.48m
2.9.81
1 Energy Line (EL)
P v2
EL=2++
2g
2 Hydraulic Grade Line (HGL)
HGL=+
P
☛关系一定是:
12
EL-HGL=
2g
在你这里:
v2
1.5²
≈0.115 m
2g
2 x 9.81
← EL 永远在 HGL上面 0.115m (在管内)

ページ27:

Ex.
Partz
EL
oh
EL
Z₁
·= 0.23 m
=038m
HGL
D= 0.1m
L=10m
-
t
Ep 12-0.05m
72 = 0.15m
Datum (7-0)
5.48
X
管中心高程z = 0.05 m
ke: 0.5
kx = 1
f = 0.025
•1) 13 31 JJ V = 1.5 1. tp = ?
(²) X Max = ?
(3) EL. HGL = ?
Hi
✓
key - kxxy - fj
v²
+ Ep
Hz
oh - ( ke + kx + f o ) ( x ) + E p = 0
·1.5²
(0.38-0.15) - (0.5 + 0.025 -10° ) ( 21981) + Ep = 0
Ep = 0.23 m

ページ28:

(速度水頭)
zike.
key 5 f 1
y
-
y
Z
2 - HGL 5715
吉)(y)=x(黄)
(21-2) - (ke+1 + 吉)(y)
(0.38 -0.05) - ( 0.5+1 +2015)
x=5.48m
(1511) = x (151)
:pump
是加壓,不是加速
=0 代表管流⇒ 渠流(自由液面)
滿管

ページ29:

Drag and Lift & 41
Fb drag force 13 $ 517 67 PA
FD - SS₁ (psino + 2 cos &) JA
=
form drag skin drag.
形状阻力 表面阻力
= pressure drag = Viscous drag
、分離流
PJA
7dA
92 cos
投影面積壓差个
PJA
7dA
* 2 drag force Max.
Felift force 移動方向
Fi
·SS₂ Paso JA
A
09⊥投影面積↓壓差↑
lift force Max.
dray force
面積↑
,
lift force
J
壓差↑
太小小
GZsing

ページ30:

無因次
Aev²
F₂ = CD
F₁ = C₁.
Aev
=W-FB
+ MD (r₁-r) = (ls (~D³
體積:
Boundary layer (B.L.)
Cp. drag coef.
C. life coef.
:
f(Re, Ma)
E:空氣彈性模數
Ma = ev²
eve
E
Re = TAU
(✔)
(x)!
Laminar BL.
wider wake 尾流大
10' > Re > 2.5 × 10 5
Turbulent B.L.
narrower wake / 2.5×105> Re
動量傳遞旺盛
分離點往後延遲
Cp
skin drag?
form drag P
Cp=
R
·L.B. L.
·T. B.
開始分離
5
2.5 × 10
10

ページ31:

EX.沉降管(settling tube)量測微小颗粒之粒徑
M = 0.075 kg
V+= 0.12
=
ls - 2300 kg, l = 900 k
假設 Re < 10
24
24
Cp =
Re
vb
24
→ b = ?
(VD) (1)
FD = C, LAU CD ( ( (70) V²) = 24M
=
"
VRE
((((70) V²)
= 3 μTLD V
F₁ = W-FB = (VS-Y) =—=~²
=
(es-Ogxp³
3μTV = (es-() grup*
D30V6
3.0.075.0.12.6
115-009
(2300-900)9.81
b = 3.43 × 105 m
0.12.3.43.102
= 3.43mn
mm
Check Re =
0.075.
4.910
✓