ページ3:

Ex.1 stagnation tube 停滯管:總水頭
=
✓
39
S.P..
V₁ = V V₂ = O
S.p. stagnation point 1 b
BE Bernoulli
Bernoulli equation
+
V²
2g
V²
g
b
V = √2gh
Kidth)
Datum 基準點 z=0

ページ4:

Ex.z Piezometer 靜壓管:高度水頭+壓力水頭
IV:量不到V水頭
BE 1~2
Pi
2
VV
J
3
4
V4 = V
=
P₂
2=0
Pz
+ = 2 +
+ Z4 +
BE 3~4
Pz
•+ 732 +
P3 = P. + r2
P3 = P4
P4
Py
P4 = rh+rd = h + d = P 4
品

ページ5:

Ex. 3 Pitot tube
litoh
BE 12
Pi
+2
+ 2 +
V₁²
P₂
Vz
+ €2 +
29
V₁²
P₂
eg
壓力計的
evi²
2
Toit 67 Pa = Pb
=
P2 - P₁
P₂ = lg l₁ + Pa
=
,
Pa - Pz - lg l₁
P₁ = eg (litch) - efgoh -PbPb = P₁-eg (l₁tah)+ efgeh

ページ6:

Pz - Pg l₁
=
P₁-eg (litoh) + efgoh
evi²
Pz - Pi
ev₁2
2
R
V₁
=
=
P2 - Pi
egt. - eg (litah) + efgoh
ef goh - egoh
ergoh
e
Jagah (-1)

ページ7:

Ex 4 Venturi tube 21
喉部
AV₁
Az Vz
Z₁
Z₂
BE 1~2
Q
Datum (z = 0)
突縮漸擴
E:L
·energy line
V₁~oh
V-floh)
P₁
P₂
+ Z₁ +
oz
+ z 2 +
P₁
V₁²
Pz
+
+ OZ +
r
29
E to it by Pa = Pb
Pa - efgoh - eg (l₁toz) = P₂,
=
Pa - Pz + lf goh + eg (litoz)
Pb
-eg
(sh+l₁) P₁₂
Pb = P₁ + eg (oh+l₁)
6/5 2/5

ページ8:

Pz+ efgoh + eg (litoz) = P₁+ eg (oh+l₁)
Pz- P₁ = eg (oh+l₁) - ef goh - eg (litoz)
Pi
eg
eg
-( PP ) = oh - ff oh - 02
=-(oh (1-(f) - oz)
eg
31-P₂
=
oh (-1)
+07
CE Continuity equation
A. V₁
=
Az Vz
V₂ = (AL) V
2
wing·ㄓㄢ())

ページ9:

r
+
31-P
Y
V₁²
Pz
+ OZ +
29
oh let.
+07
V₁²
Vz²- V₁²
只一只
Y
29
=
=
oh (-1)
( &£ -1) + 0 €
2
V₂²- V₁²
29
=
+ oz
号(1)+08
V₁
290h (1)

ページ10:

EX-5
A1 >> Az, Azzl
no in flow.
CV
VAih
0 V₂ = ?
·• h(t) = ?
h = 90cm ho·30cm
ho
雖然是unsteady,但
Ai
d = 6.4cm
JV
J.V.
77
ot
→ V₂
所以當成Steady
0 = 60cm
CE Continuity
AU₁ = A₂ V₂
Vi
=
BE
equation
Art V., V. cc Ve
Az V₂
(1~2)
大氣壓力
+ 2 +
V₁²
z
Vz
=
大氣壓力.
Pz
+ 72 +
2gh a√h
g

ページ11:

RTT const
dmsys = 0 =
dt
d
SSS ed# + $ eu dÃ
dt
C.S.
C.V.
0
=
d
dt
=V = Ah
SSS d# + $ J JA
C.V.
C.S.
out
in
dh
=
Ai
+
(A₂ V₂ - 0.)
0
dt
10 x V₂ = √2gh, A ; A,
10 =
=
Az √2gh
Ai
Jh
t
dh
- Az
√2gh.
A
dt
h = dh
()
)
=
- A= √zg dt
Aj
A₂
√zg t
A

ページ12:

16
Az
ho
Ai
()
A₂
-2 (h²-h₁²) = Airy t
Ai
A₂
2
hit) (bo² - Pi√gt)"
= no
2
A

ページ13:

Work - Energy Equation
功能方程式
stream tube
供能
P₂
V₁
72
Ep
Datum
3=0
Eppump 提供水頭
Ex
turbine耗能
消耗水頭
( f 1 13₁ + √ √ 1 ) + Ep - E₁ =
P2
(
+ Z₂+
V₂

ページ14:

EX.6
V₁ c c V z
* 0 V₂ = ?
no inflow
A1.1
> V₂
© d =
= 20cm,初始水深子。= 15m
t=5hrs,z = 0
Ep = ?
W-E equ.
+ 7 +
29
2
V₂ = √2g (z+Ep)
PTT回顾預前:)
0:
代入 v2
=
dz
dt
=
A₁
dz
dt
+ Ep
十
V₂
=
+72
+
out - in
(A+V₂ - 0)
2g (z + Ep), AAA₁
Az
: [](2+)
=
] (2 + Ep) =

ページ15:

=
√³ (2 + Ep) ³ dz - [-(AL) FJ ] || dt
=> ( Z + E₁)
(A) by t
。
√2 + Ep - √20+ E₁ = ( - ( + ) ( ) √ ] t
Zo+ Ep [ 1 ²)
=>
2+ Ep =
Zo+ Ep - [(±) (A) √ ]t
75
⇒ [ep = 115+Ep -2.55
2
(√ Ep 1065) (115 +Ep)*
Ep = 2.77 m
=
艹
.5hrs=5x3600
Sec

ページ16:

Momentum Equation ME
動量方程式
RTT (B = V₁; B = m V₁ = momentum)
d
SSS
t
I (mid) sys = F I JJ vedt + of ve vidÃ
C.V.
C.S.
dt
接觸力
4th F <
surface <+
field
超距力
tension
<
·Pressure Fp
shear ideal μ-D
→
body
force
·F₂ (9)
I. Steady flow 20
F = $ ve v· JÃ
I stream tube
C.S.
= D
Ví
A³,
V
25
F = SS v₁ ev, JA, + SS v₂ eV, JA₂ + SS V₂ CV, JA₂
A.
Az
A3

ページ17:

1. Incompensible fluid P = const.
F = ev, (-A.V₁) + e v₂ (A₂V.) AQ=V.A. - V-Az
=
evi (Q) + ev₂ Q
= CQ (V. - v.)
x-direction Σ Fx - eQ (Vox-Vix)
=
=
y-direction εFy - ea (Vay - Viy)
=

ページ18:

Q
pipe flow 管流
EX. 1 彎曲管
f = 1000 kg 1 = 107
|
Q
S
Given Q-300 — = 0.3 m²
di=300mm
dz = 200 mm
P₁ = 70 kPa
#p=0.085 m³
求流體作用於彎曲段之力?
A₁V. = AV₁ = Q
(反作用力)
V₁ = 4.24 3, V₂-9.55
m
CE
BE
|~2
P
Y
VI
29
不知
1.5.
P₂
+ Z2 +
P₂ = 18.7 kPa
福

ページ19:

ME
V₁
Fp
个个
FP₂ = P₂Az
FC
Fc fluid.
.P.A
Fex Fay
EF ✓ Fp
Fb = W = rtb
out
-Th
> Σ F₁ = F₁₁ + F₁₂ cos 60° - Fcx - PQ (-Vzcas 60° - V₁)
(上頭)
No +18.1 cs60°- Fex = 1000.0.3 (-9.55 860°-4+4)
Fox = 794 KN
fluid.
所以「反作用力」 Fful += 7.94KN→
→>>

ページ20:

Ex. 2
Fp₂
Az
d=a3m
d2=0.35/m
FP3=0 大氣壓力
FRA
FP3 = 0.
11
P.A..
CE
AV₁ = A> V₂
2
0.25
(π (%)) + 6 = (7 (33) - 1 (2)"), V₂
V2 = 19.64号
BE 1~2
Y
上
+
+
V₁²
V₁²
29
6²
9810 2.9.51
=
=
大氣壓力
Vz²
29
+ z 2 +
19.642
2.9.81
29
Fp
FP3
F
3
· P₁ = 174.86 Pa

ページ21:

ME
Fp₁ = P, A = 17 4.86 (π (233) = 12.36 kN.
ΣF₁ = Fp - F = eα ( V₂-V.)
12.36 × 10" - F = 1000 (π (13)) +6 (1964-6)
F = 6.58 FN <
障礙物 → fluid
F fluid → 障礙物 =
6.38 IN →

ページ22:

EX 3 Plane Jet on
平面射流
a
splitter
分流器
Given Q = 0.059 ans
U₁ = 305
BE 1~2.
·F Fc = ?
F14172 CV. 17 ED
V₂
12
Fux
CV
F p <.
Fcx
Fry
Fb WFN, Z
+ z t
29
=
V
好太小,忽略
V₁ = √₂ = V3
ME
+ ΣFx =
out
(1 + (+ Vocas 60°) + ((-4565 60°))
in
-
eav
x
- 1000 × 0.059 x 30
=
-
1.77 EN

ページ23:

·Σ Fy = Foy = P (£) (U₂ sin bo°) + ((~) (-Vasinbo³) - 10.0
Fry =
= 0
Fo Foye Fox
←
=
Vi在X轴上
分流器 →
fluid

ページ24:

EX. 4
Q
V₁
Fo
Fcx
CE
√3
Q₁ =Qz+Q3 Q3 = Q₁ - Q₂
BE
V₁ = V₂ = √3 = 30m
V3
30号
(£)
(承上題)
ME
S. Fox = Fc sin bo°
Fey = Fc cos bo
V z
± Σ Fx = - Fo sin bo° (<)
=
(Qz (V₂ sin bo³) + (Q3 (-V3 sin 60°) - PQ, V.
(Qz (Vz sin 60°) + (1Q₁ - Q₂) (-Vs sin 60) - (Qu
1+2Fy = Focos 60² ho
:
So not
= ( Q₂ ( V₂ cos 60 ) + ( 03 (-Vs cos 60°) - 0
= (Q₂ (Vzus 60°) + ((01-02) (-V3 cas 60°)
m
=
Q₂ = 0044 m Q3 = 0015 15, Fc 1533 kN
,
7

ページ25:

EX 5 Jet flow from a
V₂
(B
V
cart
cubic meter / second
Given Q = 0.01 cms (m²)
V = 10 m
=
10号
I⋅ m³
水受力<
·Fx= ?
·Fy?
CV
求
Fx
W
Cv
↑↑
Fr<
Fx
Fy
Fb W↓ W$= 200 N
:
WAC = 1000 × 1 × 981 N
:
BE 1~2
122
+ 721 +
~3
P✓
V₂²
172 +
Vi
- V₂ = V3
=
10号
(A ME
out from c.v. =
in to C.V..
V3
ΣFx = Fx = eQ (Vzcos 60° - √3 cos 60°) = 0
·Fx =0

ページ26:

M
=
ΣFy = Fy-weQ (V₂ sin 60°- (-V₂) sin 60°)
= 1000 0.01 (10 sinbo" + 10 sin bo")
=
173.2 N.
Fy = W + 173.2 = 1000 × 9.81 +200 + 173.2
x
Fy
= 101832 N
BME
ΣFx = Fx = lQ ( V₂cos 60°-0
out from c.v.
-in to CV.
0)
Fx = 1000×001 × 10 as bo°
X
=
·50 N
=
ΣFy = Fy-w- eQ (Vasin 60°- 0)
Fy = 1000×9.81 + 200 + 1000·0.01.10 sin 60°
=
100966 N

ページ27:

·C.V.
moving
with
Constant
V₁ = Va - Vov.
→
V₁ = √r + Vo.v.
CE 質量守恆
ME
Vc.v.
:
Ur relative velocity
:
Va absolute velocity
Ve Control volume velocity
通量就用VW!
不隨士變
dmsys = 0
d
=
dt
dt
SSS e s t + G e V r d Ã
C.V.
Steady flow
§ e Vr dà = 0
C.S.
Val = 17t
d
I m Va sys F = o III V JV
dt
=
=
-
e + S
c. S.
ff ( Vr + V cv) e V r d A
C.V
+
Ve Vr da
=
C.V.

ページ28:

Ex.b Cylindrical jet on a moving
dish
V-60号
Fp F
50mm
0.2m
[U = 12 m²
射流
射在圆盤
Fb W
(y-dir)
①欲維持0:12℃,需施力F=?
② 流體作用於圓盤之功率=
m
U = Vov. = 12 14
48号
V = Va
=
60号
• Vr = 48174
48号
Vr=Va-Va.v=60-12=481657
①BE1~2
/ +21+
48号
=
0.).
+ 72 +
2
Vz²
29
Z =
乒
V2
=
0.1 +
29
g
482
V2 = 42.98 48号
=

ページ29:

out
in
[ME Σ F₁ = F C Q (48 cos 30° - (-48))
=
(AVr (48 cos 30° +48)
0.05
= 1000 (72 (205)² 48) (48 65 30°+48)
②功率=FxV
8442N
= 8442 × Va.v.
= 8442 x 12
= 10/3kW

ページ30:

下射式閘門
EX: "
Sluice gate F 1 & 19 P9
Fan
V₂
閘門受力F=?
D
=
P..A.
F
Fe
· Fz = x y z B
F₁₂
个个
B
ry.
F3
ryz
CE Q = U₁A₁ = V₂ Az
ME
V₁
=
V₂ = a
Q
Ai
=
Q
By
a
Az
Byż
± 2 Fx = F₁ -F₂-F
Fi
F = F
F=
=
Cos O
·F = Fcos O
F<!
F₁ = Fsino
Fb - W↓
eQ (V₂-V₁)
= ea (By. By.)
2

ページ31:

Angular ME AME 角動量方程式
= Moment of ME MME D₤g t
Je RT] 57 B =
Y x V B = r x m V
把PTT的
dr x m V
1 m.
=
Yx F = Jt
dt
,
乃不變
SS ( x ) d t + f (r x V) e V d A
CV.
Y x F = $(rx v ev dA
0.4.

ページ32:

EX. 1 H H Given Q=0.3 cms (m); j<r=?
Q
V₂
AFP₂ = P₂A₂ = 1.049 N
1,5m
V₁
Q
0
F-8813N
FC
P.A, W-833N.
Foy
Fux
4948N
Fp
Fr. < Frid = Fr₂ sin 60°
·Fp₂ cos 60°
。
Fp=
GΣM. Fp₂ sin 60° 0.6 + W. 0.525 +Fp₂ cas 60° 1.5 - Fer
out
ele I-Vzsin bo ab - V₂cos 60° 1.5
in
-
0)
·P₂ Az sin bo²:0.6 + W. 0.525 + P.A. cos 60°· 1.5 - For
= 1000 0.3 (- Vasin 60° 0.6 - VGs 60° -1.5)
r = 0.61m

ページ33:

EX.2 雲梯車
y
Lx
Given l = 20m
V₂
I sin 45°
A=45°,D=20cm
↓:50
mim
Q=30号,梯+水管重:1501
求口支點所提供之支撐力<
Fx
Fy
轉矩?
Fx
=
PAF₁
· Fiy = Fi Sin 45°
Fy
Fix
=
Fi Cos 45
Fi
Fiy
Fx
Fix
F6= W = (150%) (20cm)
=3KN
V₁ = 0.955 m
V2:15.28号
CE
30
A₁V₁ = AzV₂
1000
S
BE
1~2
喜
+71 +
P² + 7/2 +
I sinks V₂
2
zg
29
P₁ = 254.6 kPa, F₁ = P₁A₁ = 8 kN

ページ34:

ME
± ΣFx - Fx + Fix = P Q (V₂-V, cos 45°)
AME
=
Fx +8 costs = 1000
Fx =
=
x = -5.22
=
0.03 (15.28 -0.955 cos 45°)
kN
eQ (0- Visin 45°)
Σ Fy - Fy + Fiy - eQ (0-
Fy + 8 sin 45° = 1000 0.3 (0-0.955 sings)
Fy =
-2.68 kN
(GΣMo = W ( ₤ c² 5 45') + T
6210 W (= cos 45°) + T = (Q [+Vz I sin 45°-0]
out角動量-in角動量
T = -14.7(KN·m)
逆時針方向

ページ35:

(噴溉裝置)
EX. 3 Sprinkler (*) » W = ? (rpm)
R=0.15m
V
三桿式
© W = 0 = T = ?
mm
R
水喷出来,它就會轉
V
8-40°
Q = 27 m²
CE
Q
=
3A Vr
√r = 6.5 13
(和噴的方白反白)
Vr
•Vt=Vcivi
rpm
rpm.
=
X
revolutions
2πL
60
=
rad
W(2)
Vt
=
60
S
V₁ = Vr + Vt
Va
V₁ = (-Vrcos 40°) +Vt.
per minute.
R. (m)

ページ36:

AME
why?
=
0 + 2 [M + = 0 - 3 ( ( $) [+ Va R ]
=
ea [
Vť
W (TUR)
60
Vr⋅ cos 40°
6.5 cos40° JR
Va=0
Va
=
-6.500540°+
W(25)
R
=
60
☹ W = 0
+2 EM₁ = -7 = PQ F-6.5 cos 40° ] R
T = 0.563 (N·m) 逆時針

ページ37:

太空船推力(Thrust)
acceleration = ?
定值
.CV
Vs
Vf
ms
+
mf
If
有效推力20.
燃料mf會越來越少
D Thrust = ?
②極限Vs=?
• Given if Toky
=
• 12 P & V₂ = ? when o
=
m
Ms+ Mfr · 8200 kg
Vf 1500 et, tb lk Vs, mf.D
=
Vs,
=
0
·t = ?
C v. 1 1 1 1 1
It S S ed v + B ef Vr dÃ
dt
=
dt
0
d
:
移项
dt
C.V.
(m₁ + mp) + [mf-0]
↓ms不隨士改變
dmf
dt
=
-
-mf dmf = - mf dt
"mfo
mf-mfo
--
mft
mf = m fo - mf⋅ t

ページ38:

ME
=
dheque.
domů ) sys
dt
沒有外力 0
=
=
d
Thrust
"
C.V動量變化率。推力動量通量=mf.Va
=
<ms+mf
ful
I t JJ V s e d V + B Va Gp V r d Ã
dt
·C.V.
C.S.
It [(mstmf) Vs] + [Va. mf -0]
"
=
=
Thrust
+ Va mf
質量流率的=
Jm
dt
+ Va Vr + Vov = (-V+) +Vs
1 Thrust = -Va mf.
V g m J F
不能ThrustF
m
=
m
=
-
(Vs-VF) mf
(Vf - Vs) mf >o
'
D
=
$11952
(M; +mf) d Vs
dt
dvs
dt
II m 1 x
Va
+ Vs (dmf) + (Vs - Up) m f
-mf
sn+
0 = (ms+ mf) It mf Vs + Us mf - Vf mf

ページ39:

②
dvs
(ms+ Mf) dt
a =
Vf.mf
Ms+ Mf
=
Vf mf
當有效推力 Thrust = 0
Thrust
=
(V₁-Vs) mf = 0.
a
=
JVs
dt
V₁ = V₂
Vf mf mf Vf
=
Ms+ Mf ms+ (mf.-mft)
70×1500
=
dt
8200-700
70.1500
=
8200-70t
Vf
=
1500
Mox 1500 800 not t
8200-700
= 70x1500 (- -) (In 18200-700 | - In 8200)
8200-700
Let u=
8200-70t
du=-70dt
|= -l n
8200
8200
e=
8200-700
t = 74 s
=
1.23 min

ページ40:

原型V.S.模型
prototype model
無因次參數 dimensional
雷諾數 Re
VL
=
福祿數: F=
192
無因次化方程式
eg.
x
=
無因次的
U
to
Po
=
=
"1
t
Zt I + <=
lev³)
P
hu
Parameters
:
M
e
(特性)
L三特微長度 Characteristic legth
V=特微速度
X = XoL
U = U₁ V
t = t₁ ( ~ )
=
·P⋅ P. ((v)
Po

ページ41:

相似律
EX. 1-1 Given Lr = LL, Dr VR 2 Reynolds #ART
0 Vr = √ R = ?
Vm
VpLp
"P
=? (Re)
(Re)p
Vm Lm
Vp Up L
Lpvm
Vm
© tr = tf. ?
tp
告
Vm
=
=
(Re)m
Vr
Ly
Vm
±· 1. ( 2 ) (v.). (17)
tm
=
Lr
Dr
© ar = ap = ?
a = 1/144
ap
am
am
Vi
Qr · Of = ?
QR
Qm
Qm
=
Q = AV
Apv₂ = ((r²) (11) = L₁dr
Am Um

ページ42:

EX 1-2 Fronde TBTK 19, Given Lr = LP gr = gt
,
gm
VP
Vm.
• Vr = ?
19pLp
√gmLm
Vp
√gp Lp
Vm
=
√9mlm
L
③tr = ?
t =
tp
tm
Ⓒ Ar
=
ap
am
:?
a
Vm
t
乖乖
Li
gr
© Qr = ?
Q = AV
Qp
Qm
=
ApVp
Am Vm
=
L
gr
Li gr br
=
gr

ページ43:

EX. 2 Dray force JE
拖电力
✓ A= Frontal area
· TUD²
e
N
→后
FD
•FD = function?
②相似伴?
② 如何設計實驗?
du
Z = M
:dy:
· [ M (= ] = M [ x ]
F₁ = [11], (= [ + ], M = [ 1 }], D = [L], V = [ ]
[+],M=[],D=[],v=
• F₂ = fle, M, D, v)
n-1-5-3
= 2
Tv₁ = f (Th₂)
Tufl FD, C, D,V)
Th₂ = f (M, e,D,
πL, [0] = [11] [
TV
=
FD
V.)
n=5
Me
D
T V
C
7. [•] = [4] [ ] [ ] [ ]
Th₂ = MeD" V"
,
1+9=0 a=-1
·1-3a+b+c=0,b=-2
2+0=0
C=-2
H+9=0,9=1
·-1-3 a + b + c = 0; b = -1
1+0=0,0=-1

ページ44:

F₂
M
eb² v² = flexv) = f(p)
Fp
=
Hev · fire) · Relat
CD
b² v²
=
Fb = b²ev fire)
Dev² CD
CD & drag coefficient.
C₂ = FD
(Dev)
✓
C₁₂ = f(Re)
> Re

ページ45:

X4 方程式無因次化(一維平流擴散方程式)
JC
=
Ht
1b Advectim- diffusion equ.
口袋
:diffusion coef..
握散係數
车流
DLX Cb. H. V Z Z π t ñ y z t
C₁ =
to
=
C = CoCh
号
t
t = to (#)
:
孔。
"
x
H
代回:d(CoCL)
同业
d (to (#))
X = X₂H
=
D
J (Co Cb)
d(XOH)²
J (Co (b)
-V
J (XOH)
CLV
b
J Co
d to
VH
jd Xo²
dxo
JCo
J. Co
Pe
8Xo

ページ46:

② 白金漢兀定理,C=f(cb,D,v,x,H)
=
C · [11], C₁ = [ 11 ], D= [+]
V-[÷],x=[1]
,
H- [L]
=
C = f (cb, D, V, X, H) n = 6
n-k=3
M Cb
L
k=3
Th₁ = f (Th₂, TU3)
T V
Tu = flc, Cb, H, V)
LM
TV₂ = f (D, Cb, H, V)
TV3 = f(x, Cb, H, V)
πL. [0] = [^] [M] [L] [7]
Hα= 0, a = -1
3-39+b+c=0
C = 0, b = 0
The [0] = [ 4 ] ([^^ ^] ^ [1] ^ [ + ] 2-3a+b+c=0
HC=0 C=)
C
C
a = o, b -1
=
C
Th₂ [
[]:
=
[L] [+]
9=0
b=-1
C = 0

ページ47:

c flu, # ) = f ( x )
=
cb
VH
H
H
• Pellet #12 13
11 71 122 (Pe) p = (Pe)m
31-7 7 12 Xp Xm
HP
=
Hm