أساسيات قدرة الموائع
-
Upload
mohammed-enab -
Category
Documents
-
view
72 -
download
3
Transcript of أساسيات قدرة الموائع
אאאא
FFEE
١٦٢١٦٢
א ١٦٢
אאFE
،،אא،אW
אאאאאאאאאאאא،אאאאאא
אאאאאאאאאאא؛אא
אK אאאאאאא
א ،א אאאאאאאא،אא
א א ،א אא א א א א א א אא א א א
אא،אאאא،אK
אא?אאFE?? ? א א א א אא
אK אאאאאאא،א،אאאא
אאאאאK
אאאא؛אK
אאאא
א ١٦٢
אאFE
אאאאKאאאאאאאFEאאאאאאK
אאאאאאאא،אאא– JK
אאאאאאאאאאאאאא
אאKא،אאאאאאאאK
אאאאאאW
• אאאאאאאאK
• אאאK • אאאאאK • אאאאאא
אאאאK • אאאאאאאא
אאאאK • אאאאאאא،א
אאאאK אאאאאאאאא
אאאאK
אאאאאאאא
אאאא
אאא المؤسسة العامة للتعليم الفني والتدريب المهني
אאאא
א
אא
א
١
א ١٦٢ אא אאFE אאאא
- ١ -
אאW א א אא א אא אאKאאאאאא
אאW אאW
o אאאאאאאK o אאאאאאK o אאאK
אאאW
א١٠٠א٪
אאW ٣
אאW אאאK
אאW א،אאאK
א ١٦٢ אא אאFE אאאא
- ٢ -
W אאאאאK
אאאאאאאאאאאאאאKאאאאאאK
אאאאאK ،א،א،א،א،א،אא،אא
K Jא JאאK אאאFEאK
אאאKאאאאאאאאאK
אאאאאאאאKאאאאInternational
System Of Units"אאאFSIEאK אאאאא
אאאאאאאאאאאאאאאאאאא
אאKאאאאאאFSIEK
א ١٦٢ אא אאFE אאאא
- ٣ -
אאW
אא،אאאאאאאאאK
אאאאאWאאאאW
WאאW
א אא אא ١א Length L L m L
٢א Mass m M Kg M
٣א Time T T Sec. T
WאאW ١א Area A A = L . L m2 L2
٢א Volume V V = A . L m3L3
٣א Density ρρ = m / V Kg/m3 M/L3
٤א Velocity ψ ψ = L / T m/sec L/T
٥א Acceleration a a = ψ / T m/sec2 L/T2
٦א Force F F = m . a N (M.L)/T2
٧א Weight W W = m . g N (M.L)/T2٨אא Specific Weightγ = ρ . gγ N/m3 M/(T2.L2)
٩א Pressure P P = F / A = . hN/m2 M/(T2.L)
١٠אFאEEnergy (Work )E E = F . L J (M.L2)/T2
١١א Power IP IP = E / T W (M.L2)/T3
١٢א Flow Rate Q Q = V / T = v . A m3/secL3/T
א ١٦٢ אא אאFE אאאא
- ٤ -
אW
hrmile60
secm
אW 1ft = 0.3048m ,1mile = 5280ft ,1hr =3600sec אאW
13084.0 =×ftm
15280 =×mile
ft
1sec3600 =×hr
אאאFאE،K
אאאאא،אאאW
( )( )( )
⎟⎠⎞
⎜⎝⎛=⎟
⎠⎞
⎜⎝⎛=⎟
⎠⎞
⎜⎝⎛⎟⎠⎞
⎜⎝⎛⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛=⎟
⎠⎞
⎜⎝⎛
sec8.26
sec360052803048.060
sec3600152803048.06060 mmhr
milesft
ftm
hrmile
hrmile
אאאאאאאא
אאאאK אאאSIאאא
אK
א ١٦٢ אא אאFE אאאא
- ٥ -
אאW אW
•
2
3
632963
sec8.9
10001sec3600min601
121255.21
1010101010101
mg
Lmh
inftmmcmin
mmmcmGmMmkmm
=
=
===
======== −−− µ
אW
• 4 in = ……………... mm mminmmmmcmmm
incmin 1004100
111105.24
110
15.2
14
=⇒=⎟⎠⎞
⎜⎝⎛
××××
=⎥⎦⎤
⎢⎣⎡ ××→
• 10 m = ……….…… in inminincm
inmcmm 40010400
5.211110010
5.21
1100
110
=⇒=⎟⎠⎞
⎜⎝⎛
××××
=⎥⎦⎤
⎢⎣⎡ ××→
• 10 mm = ……….…… µm mmmmmm
mm
mmmmm µµµµµ 10000101010
1010
101011110
101
101
110 431
36363 =⇒===⎟⎠⎞
⎜⎝⎛
××××
=⎥⎦⎤
⎢⎣⎡ ××→ +++
−−−
• 1000 µm = ……….…… mm
mmmmmmmmmmmm
mmm 1100011010
11110101000
110
110
11000 0363
3636
=⇒===⎟⎟⎠
⎞⎜⎜⎝
⎛××××
=⎥⎦
⎤⎢⎣
⎡××→ +−+
−−
µµ
µ
אW • 10 in/sec = ……………... mm/min
min15000
sec10
min15000
min111160105.210
min1sec60
110
15.2
sec110 mminmmmm
cmmm
incmin
=⇒=⎟⎠⎞
⎜⎝⎛
××××××
=⎥⎦⎤
⎢⎣⎡ ×××→
• 120 km/h = ……………... m/sec
sec3.33120
sec3.33
sec6060111110120
sec60min1
min601
110
1120 33 m
hkmmmh
kmm
hkm
=⇒=⎟⎟⎠
⎞⎜⎜⎝
⎛××××××
=⎥⎦
⎤⎢⎣
⎡×××→
אW • 10 m/sec2 = ……………... in/min2
24
2222
2
22
22
2 min10144
sec10
min1440000
min15.21160110010
min1sec60
5.21
1100
sec110 inminin
cmin
mcmm
×=⇒=⎟⎟⎠
⎞⎜⎜⎝
⎛××××××
=⎥⎦
⎤⎢⎣
⎡×××→
אW
• 45L = ……………... mm3 36363
3
93
3
3
3
33
3
3
104545104510
10451101
10001451
1000101
145 mmLmmmmmm
mmm
LmL
×=⇒×=⎟⎟⎠
⎞⎜⎜⎝
⎛ ×=⎟⎟
⎠
⎞⎜⎜⎝
⎛××
××=⎥
⎦
⎤⎢⎣
⎡××→
א ١٦٢ אא אאFE אאאא
- ٦ -
אאאאאSIW
• אא (1m) FL E • אאא(1kg) FME • אא(1sec) F TE • אאא(1k)
אאאאאאאW
אאאאאW
• אWאאאFm3E • אWאא(m/sec)K • אWאNewton (N)،אא
אאאא(m/sec2)K • אWאאאKאאא
L(N/m2)K • אWאאאא
אL(kg/m3)K • אאWאאאm3/kgK • אWאאK(N.m)א(J) K • אWאאאא(Watt,W)K
אאאW אאא،
אאאאאW • אK • אK • אK
א ١٦٢ אא אאFE אאאא
- ٧ -
אאאאאFאSIKE אאאKאאאאא
F1 Kg E1 Kpa אK W
אZא×א a . m = F
אאאFאE،אאאאW
אZא×אא g . m = F
22 sec.81.9
sec8.911 mkgmKgKPa =×=
אאאFאSIEאאאNאFK אNאאאא1 Kgא1m/s2K
22
.1111
smKg
smKgN =×=
NKP 81.91 = אאdaNNKPa 1101 =≈
אW אאאא،אאאאK
אZP אZF אZA
AFP =
א ١٦٢ אא אאFE אאאא
- ٨ -
א،אKP/cm2
FאE1KP/cm2 = 1atm
אאאא،W
1bar = 10 N/cm2 = 1 daN/cm2
1 bar = 1.02 Kpa/cm2
1KPa/cm2 = 0.98 bar
אאאאאFאSI E،אאFNEא
m2،אאאPa
1Pa = 1 N/m2
אKאאאKאאאאbar אK
1 bar = 100000 Pa
אpsiFEאW
1 bar = 14.5 psi
אאאאאאאאKא
אא،אbarאאKאF١١EאאאאאK
א ١٦٢ אא אאFE אאאא
- ٩ -
F١١Eאאאא
אאאאאא
אאאW אאW
א אא
א א א
א אא
decade 10 deci d 10-1
hecto
h 102 centi c 10-2
kilo k 103 milli m 10-3
mega
M 106 micro
u 10-6
giga G 109 nano n 10-9
אtera T 1012 pico p 10-12
א ١٦٢ אא אאFE אאאא
- ١٠ -
אא،אאאאאאאFאE
W
mag
Fc
1=
FאmאaאgcאאאאאאאKאsiאא
W
2sec1111 mkg
gNewton
c
××=
W 2sec1
×=
Newtonkgmgc
אאW
2sec111 ftgIb
gIb m
cf ××=
אא(gc)אא2sec
.174.32
f
m
IbIbftא
אאsiאK אאאאאאBtuא
אאsiW
1 Btu =1054.35 J(or N.m)
אאאא(SI System)W אאאאW
Kאא •• אאK • אאאאאאK
א ١٦٢ אא אאFE אאאא
- ١١ -
• אאאאאkgNK
• אא،אאJ ،KאW،אN.mא
אW
אא400 kj،،אאאwK אW
WJhrKJ
JhrKJP
hrKJPPower
2.222sec
2.222sec3600
1000800
4002,
==⎟⎠⎞
⎜⎝⎛⎟⎠⎞
⎜⎝⎛⎟⎠⎞
⎜⎝⎛=
×=
W אאW
E1 = 4000 J E2 = 10 W.hr
E3 = 20 kN.m
א KJBtuK אW
( ) ( )
( ) BtuKJ
BtuKJE
KJE
mKNKJmKN
jkj
hrhrJ
JKJJE
87.56055.1160
6020364
..20
1000sec3600
sec10
10004000
=⎟⎠⎞
⎜⎝⎛=
=++=
⎟⎠⎞
⎜⎝⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛⎟⎠⎞
⎜⎝⎛+⎟
⎠⎞
⎜⎝⎛=
∑
∑
∑
אאאאאאאא
אאאא
אאא المؤسسة العامة للتعليم الفني والتدريب المهني
אאאא
א
א
אא
٢
א ١٦٢ אא אאFE אאאא
- ١٠ -
אאWאאאאK
אאW אאW
o אאאא o אאאאאאא
אאK
אאאW אא٩٠٪
אאW
٣
אאW אאאאאK
אאW
א،אאאK
א ١٦٢ אא אאFE אאאא
- ١١ -
W אאאאאאאא
אאאאאאKאאאאאאאאאאאאאאK
אאאאאKאאW • אאWאאאאאK • אאWאאאאK
אאאאא
אאאאאאאאאאאאאא
אKאאאאאאאאאאאאאאאאא
אאKאא،אאאאאא،א،אאKא
אא،אאאאאK אאאאאא
אאאאאKאאאאאאK
א ١٦٢ אא אאFE אאאא
- ١٢ -
אא ١LאρDensity:
אאאאאאKW
אZאLאZ3m
kgVm
=ρ
אא4אc1000 kg/mאאא 20CO،1.2אkg/mFאאאאאE
٢LאאγSpecific Weight :
אאאאאאאאW
אאZאLאZ3m
NVW
=γ
אאאW
אאZא×אאZ
Vmgg =×= ργ
٣LאאvWSpecific Volume
אאאאאאאאאאW
אאZאLאZkgm
mVv
31ρ
==
א ١٦٢ אא אאFE אאאא
- ١٣ -
٤LאאSGWGravity Specific אאאאאאא
אאא(4C0)
אאZאLאZw
fSGρρ
=
אאאK
אאאאאאW
אאTRmp ××=×ν
W
אWRTp
=ρ
W
אא2mNp = אא287(א( Kkg
JRR = אאאT(K)
א3mkg=ρ
F٢ J١WE 6.3mKא4m،א2cmאאWאא אא9772kg،אK
אW אאW
3mkg
Vm
=ρ
א ١٦٢ אא אאFE אאאא
- ١٤ -
kgm 9772= אאאW
hdV ×= 2
4π
W d Zאאא،hZאאא
32 31.116.32
4mV =××=
π אאאW
386431.11
9772mkg
Vm
===ρ
F٢ J٢E
אא،אאאאאא1000kg/m،א6750 kg،אא
FאאאEK
אW אW
אL אWאH
אאW2אWFאאEאWFאאEאאKאVW
322 wwwwhwlV =××=××=
Vm
=ρ
א ١٦٢ אא אאFE אאאא
- ١٥ -
3267501000
w=
375.3200067503 ==w
mw 5.1375.33 ==
mwl 0.35.122 =×=×=∴
mwh 5.1==∴
F٢ J٣E אאא1.6k،אאאאאK
אW
אאא1000cm3 (0.001m3)
אW
3800001.02
6.1mkg
Vm
f =×
==ρ
א ١٦٢ אא אאFE אאאא
- ١٦ -
אאאאאאאאW
8.01000800
===w
ffSG
ρρ
אViscosityW אא،א
KאKאאאKאאא،אאאאאאK
אאKאאאאK
אאאאאאK
F٢١Eא
אאFF٢١EEא
UאאyאAאאאFK
א ١٦٢ אא אאFE אאאא
- ١٧ -
אFShear StressאKאאwτאW
אZאLאAF
w =τ
אאאאאאW
dYdu
wατ W
אZ
dydu
w µτ =
µאאא،
אאאאאKאW
אאZ⎟⎠⎞
⎜⎝⎛
⎟⎠⎞⎜
⎝⎛
= 2
sec.m
N
dydu
wτµ
אאFKEFKEFאESecPa
mN .sec.
2 ==µ
אאאאאאFאECinematic Viscosity
אאZ⎟⎟⎠
⎞⎜⎜⎝
⎛=
sec
2mρµγ
אsec
2mK
א ١٦٢ אא אאFE אאאא
- ١٨ -
אאאאאאאאאאKאאא
אאאKאאאאאאK
אאאW
אאאKאאאאאאאאאאא
אאאKאא،אאאאאא
אאאאF٢ J٢KE
F٢ J٢Eאאאאאא
אF٢٣אEאF٢٣Eאאאאא
אאאKאK
א ١٦٢ אא אאFE אאאא
- ١٩ -
F٢ J٣ JEאאאאאא
א ١٦٢ אא אאFE אאאא
- ٢٠ -
F٢ J٣ JEאאFאEאאאא
א ١٦٢ אא אאFE אאאא
- ٢١ -
F٢ J٤WE א אאא،א
sec1100=
dYdu1א
אא10-3 pa.secK אW
Padydu
1.010010 3 =×=∴
×=
−τ
µτ
א ١٦٢ אא אאFE אאאא
- ٢٢ -
אאאאאאW
אאאW א،אא،אאאK
אאאW
א0.12m3אאא0.15m³א0.2m³אאאא1.15kg/mKאאאאאFKאאאאאא27501500
997אאKE
אאאW FEאאאאאאאא1/sec100
אאאא.0.001 pa.sec FEאא0.85אא
2.87×10¯³ N sec/ m²
אאאאW אאא،אאא
5.00×10¯4 N sec/ m² א40C0
אאאאW
אאאאW
אאKאאאKאאאאאKאאאאKא
אאאאK
א ١٦٢ אא אאFE אאאא
- ٢٣ -
אאאאW אאאאאאאא
אKאW
vVm 1==ρ
אאW
ρ1
==mVv
אאאאאאאW Vm ×= ρ
אאW = 2750×0.12 =330 kgmg
אW
= 1500×0.15 = 225 kg ms
אW mw = 997×0.2 = 199.4 kg
אאW
= 1.15×0.53 = 0.61 kgma
אאm totalW
m total = 755 kg
אאW
37551
755m
kgVm
total
totaltotal ===ρ
א ١٦٢ אא אאFE אאאא
- ٢٤ -
אאאאאW
kgm
mVv
total
totaltotal
3001325.0
7551
===
אאאאW
Eא JאאאאW
dydu
×= µτ
τאµאdyduאאאK
אאW
τ = 0.001×100 = 0.1 Pa
E J אאZ⎟⎟⎠
⎞⎜⎜⎝
⎛=
sec
2mρµγ
3850100085.0mKg
=×=ρ
⎟⎟⎠
⎞⎜⎜⎝
⎛×=
×== −
−
sec103.3
8501087.2 2
63 m
ρµγ
אאאאאW אאאF٢ J٣ JE،אא
5.00×10¯4 N sec/ m² אא40C0אאW
Benzene א
אא
אאאא
אאא المؤسسة العامة للتعليم الفني والتدريب المهني
אאאא
א
٣
א ١٦٢ אא אאFE א
- ٢٥ -
אאWאאא אאK
אאW אאW
o א Jאאאא Jאאא o אאאאאFEK o אאאK o אאאWאא JאK o אאאאK o אאאאאK
אאאW
אא٩٠٪
אאW ٦K
אאW ١ J אאאאK ٢ J אאאאאK
אאW
אאאאאאאאK
א ١٦٢ אא אאFE א
- ٢٦ -
W אאאאאאאKאאא
אאאאאאאאאKאאאאK
אpressure
אאא،אK
( )PaPascalmN
mN
AFP
=⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛=
2
2
W
אא)( paP = אאא )(NF =
אאאא)( 2mA = W
( )211 mNpa =
( ) kpam
Nbar 1001000001 2 == F١_٣E אFpistonE5mm1kN٣١K
אאאK אW
אאאאK
א ١٦٢ אא אאFE א
- ٢٧ -
2
4dA π
=
barKPaPmKNP
P
AFP
09.5509
509
10504
1000
2
62
==
=
××=∴
=
−π
١_٣١_٣
אאאאW
אאאאאאאא،אאאא
אאאKאאFaEאאFbEאאאFcEאאFdEF٣٢EK
א ١٦٢ אא אאFE א
- ٢٨ -
אF٣ J٢Eאאאא
FEאPressure HeadW אאאאאאאאאK
אאאאאאאK אאאאאאאK
٣٣א
אאאאאאF٣٣EFρE
אאאFFEאFmEאFgEאאאFpEאW
hgP ××= ρ ( )hgp ∆××=∆ ρ
אאאh
א ١٦٢ אא אאFE א
- ٢٩ -
F٣٢E אאאאא300cm 250cm450cmא،
אK1000Kg/m2 אאאK אW
אאאאK
F٣٤EאF٣٢E
gmF ×= ( ) gVF ××= ρ ( ) ghAF ×××= ρ
23 sec81.945.030.025.01000 mmmm
mkgF ××××=
NF 331= אאאW
2440025.030.0
331mN
AFp =
×==
אאאW hgP ××= ρ
mmmkgP 45.0
sec81.91000 23 ××=
Kpa
mKN
mNP 40.44.44400 22 ===
אאאK
א ١٦٢ אא אאFE א
- ٣٠ -
F٣٣E AB 300m200mאKאאאא
א31023mkg
אW
אאאאאאאאאאאאK
אA AA hgP ××= ρ 30081.91023 ××=AP PaPA
610011.3 ×= אא B
BB hgP ××= ρ 20081.91023 ××=BP PaPB
610007.2 ×= אאאW
PaPP BA666 10004.110007.210011.3 ×=×−×=−
אאאW hgPPp BA ∆××=−=∆ ρ
( ) Pa610004.120030081.91023 ×=−××=PA-PB
F٣٤WE אאF(101.325kN/m2W
• 1000kg/m3K • א13.6K אW
אW אאF101.325kn/m2E،אF1000kg/m3E،אאF13.6E،
אF9.81m/sec2KE
א ١٦٢ אא אאFE א
- ٣١ -
אW אאאא،אאאאK
אW hgP ××= ρ
23
2
sec81.91000
100000325.101
2
2
mmkg
mN
gPhoH
oH
×
×=
×=ρ
mh oH 33.102=∴
אאא10.33 mK
אאאא،אW
אאאאאאאW 6.13×= HgHg ρρ
36.131000 m
kgHg ×=ρ
א א א א אW
( )23
2
sec81.910006.13
100000325.101
mm
kgm
NhHg
⎟⎠⎞⎜
⎝⎛ ×
×=
hHg = 0.76 m
אא0.76 mאאא10.33 mאאאK
א ١٦٢ אא אאFE א
- ٣٢ -
אאאאW אאאאאאאאאאK
אאאאאאK אאאאאאFאאEא
אאאאKאאאאK
אאאאKאאאאאאאKKאאא
אFStandardEאאא 1.013 bar101.3 kN/m2אאאאאאK
F٣٥E אא 3.66m0.61mאא٣٥،
אאא،אאאאאאאאאא،אאאא،א 1000kg/m3
אW , 917kg/m3אאW101.3kN/m2K
א ١٦٢ אא אאFE א
- ٣٣ -
F٣٥EאF٣٥E
אW אF٣٥EאP2אאאאא،א
P1אאאP2אאאK P2 = P0 + P2g h2
P2= (101.3 X 1000 N/m2) + (917 kg/m3) . (9.8 m/sec2).(3.05m) = 128737 N/m2.
אאP1אאW P1 = P2+ P1gh1
P1 = 128737N/m2 +(1000 kg/m3).(9.81 m/sec2).(0.61m) =134721.1 N/m2
אאאא،אאאאאאW
P1(gauge) = P1 - P0(atm)
= 134721.1-101.3 × 1000 = 33421.1N/m2
אא3.34 kN/m2
א ١٦٢ אא אאFE א
- ٣٤ -
אFPressure MeasurementE א،אאא
אKאW
אFThe BarometerE
F٣٦Eא
אאאא،אF٣٦Eא
،א،אאאFpEאאאאא
אאאKאאאאאאאאאאאאא
אאאאאאאאאאאאאאK
א hאא ρא،אאW
P = ρ × g× h
א ١٦٢ אא אאFE א
- ٣٥ -
gאKKאאK אאאא1.013 barאאאא
אW
1.013 × 100000 = 1000 × 9.81 × h
= 10.326m81.91000
100000013.1×× h =
אאא10.326mאאאאKאא
אאאאא13.6אKאאאאW
1.013 × 100000 = 13600 × 9.81 × h
= 0.76m = 760 mm = 0.76 m
81.913600100000013.1×
× ∴h =
אא760mmאF760 mm HgEK
א ١٦٢ אא אאFE א
- ٣٦ -
אאThe Manometers )E : אאאאאאK א
UאאאאאאKKאאא
KאאאאאKאאאאאאאK
אאW
אF٣٧EאKUאאאאאאאאF٣٧KE
BאCK אBאאאאאhK
אCאאאאK
PB = PC = P0 + ρHg g h
F٣٧Eאא
א ١٦٢ אא אאFE א
- ٣٧ -
אאDifferential Manometer אאא
KאF٣٨EאאKאאאאFhEK אDאCK אDאP2אאאhאאZ אCא P1אאאFZ + hEK
P1+(h+Z)ρAg =P2+ρBgh+ρAgZ
P1+ P2= ρBhg +ρAgZ - ρAgZ - ρAgh
F٣٨Eאא
P1 – P2 = (ρB - ρA)gh
אאאא،אAאAאBKאאW
P1-P 2= ρB × g × h
א ١٦٢ אא אאFE א
- ٣٨ -
אאWInclined Manometer אאאאאKא
אKאאאhX Sinθ XאאאθאאאF٣٩EK
P1- P2 = ρg X Sinθ
F٣٩Eאא
אאFאאאEW
אאאאPKאאאא،אאאאK
אאאאאאKאPאאhאאρא
אgK אאאאאאW
P = h . ρ .g
א ١٦٢ אא אאFE א
- ٣٩ -
F٣١٠Eאאאאא
אאאאאאא،א
אאאאאאF٣١٠KE
P1 = P2 = P3
אאאKאאאאאFA1 = A2 = A3Eאאאאא
FF1 = F2 = F3KE
אאFE F AF٣١١E،
P אאאאא،אK
AFP =
א ١٦٢ אא אאFE א
- ٤٠ -
F٣١١Eאא
אא،אאאאKאאא
KאאK،אאאאאאK
אאאאאאא،אאאאא،אאא
אKא،אאאא10 m א1 bar K
אאאW אאא،א،אאK
F٣١٢אEאאאאאK
F٣١٢אEאאא
א ١٦٢ אא אאFE א
- ٤١ -
אF٣١٢EאאאאאאW
F٣١٢EאFEאא
אF1אא A1 P،W
1
1
AFP =
אPאא،אA2KאF2FאאאKE
2
2
1
1
22 .
AF
AF
APF
=
=
W
1
2
1
2
AA
FF
=
אאKאאאאKאאאאאא
א ١٦٢ אא אאFE א
- ٤٢ -
K אא،אF1אA1 ،אאא
אF2FאA2E،אאFאאאאKE
W אא
1
2
2
1
AA
SS
=
אאא،W
W1 = F1 × S1 W2 = F2 × S2
א ١٦٢ אא אאFE א
- ٤٣ -
אאW
F٣١٣Eאא
אF٣١٣EאאאKא
P1 אA1،אאF1KאאאאאP2אA2KאאW
F1 = F2 = F
W P1 . A1 = F1 P2 . A2 = F2
W P1 . A1 = P2 . A2 W
1
2
2
1
AA
PP
=
אW אאK
א ١٦٢ אא אאFE א
- ٤٤ -
אאאאW
F٣١٤Eאאא
אF٣١٤EאאאאK אKאא،אאאK
אאאאKא،אאא،א،אאאKאאא
אKאאאאאאאאא،אKאאאא
אK אאאאאKא
א،אאF٣١٤E،אאאא،אאK
אא،אאKאאW o אאאK o אאK o K
א ١٦٢ אא אאFE א
- ٤٥ -
KאאאK
אאF٣١٥KE
F٣١٥Eאא
אאא،אא،אW
• FאאEK • FאאEK • אFאאאEK
א FאE אאF אא K Eא אאK
אאאאאאאKאאאא،אאK
א ١٦٢ אא אאFE א
- ٤٦ -
אאאאאאK אאאאאאאאאאאK
אאאאK
אאאאאK
אF٣١٦Eאאאאא
F٣١٦Eאאאא
א ١٦٢ אא אאFE א
- ٤٧ -
אאW אאא،
א K אאא،אאPאK
אאKאאאאאK
F٣١٧EאאאK
F٣١٧Eאא
אאאאAאD
B،אאאdKאBאאאאא AאאKאאאBאאא b,a K
אאאQ،אאdF1 אP1KאאאאאW
baQF ×=1
QאאאאK אאP1אאF1 W
א ١٦٢ אא אאFE א
- ٤٨ -
21
2
1
1
11
4
4dF
d
FAFP
××
=⎟⎠⎞
⎜⎝⎛
==ππ
P1 = P2 = P
א א א א א
אאאאF2אאאW
2
2
2
21
2
1212 44
4 dD
baQ
dDFDPAPF =
×××××
=×
==πππ
אאאאאא،אאאK
אאאאא،W
2
2
2 dD
baQF ××= ξ
ξאאW
80.085.0 ≥≥ ξ
א ١٦٢ אא אאFE א
- ٤٩ -
אאאאW אאאאאאאא
אאאK
F٣١٨Eאאא
F٣١٩Eאא
א ١٦٢ אא אאFE א
- ٥٠ -
F٣٢٠Eאאא
F٣٢١Eאאאאא
א ١٦٢ אא אאFE א
- ٥١ -
F٣٢٢Eאאאאאא
F٣٢٣Eאאאא
F٣٢٤Eאאאא
א ١٦٢ אא אאFE א
- ٥٢ -
F٣٢٥Eאא
א ١٦٢ אא אאFE א
- ٥٣ -
אאא
אאאW FE א،؟אא FE אא, 7.5cmאאא
6000N؟אא FE אאאאא7.5 m
1206 kg/m³ אאאא1 Mpa؟ FE א150 kpaאאFאE 95 kpaK
אא؟
אאאW אאא101.325.א kpaא999kg/m³ K
א؟אאא
אאאW אאא750 kg/m³10³kg/m³K
אא3mא2m،אאאאאאא אאKאאא1barK
אאא
א ١٦٢ אא אאFE א
- ٥٤ -
אאאאW אאאאא،אF א100 N
אא،אF2א؟אאאא
אאאא
אאאW
אאאאW FE
• אאאK • אאאאHאאK
FE אאאW
AFP =
אאW ( )
KPaPaP
mDrA
1358135808004418.06000
004418.0075.044
2222
≈==∴
=×==×=πππ
א ١٦٢ אא אאFE א
- ٥٥ -
FE
אאאFE
אאאאאאאאאאאאא
אאאW
KPaPaP
hgPPPP OiltopOiltop
7.10881088704)5.781.91206(1000000
)(
==××+=
××+=+= ρ
p אאאK
FE אאאאHאא
KPaPPP atmgbs 24595150\ =+=+=
אאאאW
mh
hhgP
34.1081.999910325.101
81.9999325.1013
=××
=∴
××=××= ρ
אאאFא13600 kg/m³E
7.5 m Oil
א ١٦٢ אא אאFE א
- ٥٦ -
hhgp
××=×
××=
81.91360010325.101 3
ρ
h = 0.76 m = 76 cm אאא١٠٧٦K
אאאאW
אאאW
( ) ( ) kPaPaP
PPP
gage
WOilgage
5.44500100037502 ==×+×=
+=
אאאאW
kPaPkPaPabarP
kPaPaP
PPP
t
atm
gage
atmgaget
5.1041005.41001000001
5.44500
=+=∴===
==
+=
אאאאאW
אאF1FאאאאאEאאC
אאאאW
(0.33m)(100 N) – (0.03m) F1 = 0
Nm
NmF 110003.0
10033.01 =
×=
אאאאאW
א ١٦٢ אא אאFE א
- ٥٧ -
1
2
1
2
AA
FF
=
P1 = P2 = P = F1/A1 =F2/A2
F1= P1A1= 1100 N
P1 = 1100/A1
26
211 1022.6
4
11001100mN
dAP ×=== π
P1= P2
F2 = P1 A2
( ) kNmmNF 22.1205.0
41022.6 2
26
2 =×××=π
אא
אאאא
אאא ة للتعليم الفني والتدريب المهنيالمؤسسة العام
אאאא
א
٤
א ١٦٢ אאא אאFE א
- ٥٨ -
אאWא אאאאאאאאK
אאW אאW
o אאWאאאאאא Jאאא–אא J
אאאK o א JאאK o אאאאFE J
אאאK
אאאW אא٨٠٪
אאW
٦K
אאW ١ J אאאאאאאK ٢ J אאK
אאW
אאאFאאאEאאאאK
א ١٦٢ אאא אאFE א
- ٥٩ -
W אאאאאאאאאאאK
אאאאאאאאאאא،א
אאאאאאאK
אאאאTypes of Fluid Flow
אאאאאאאאאאאאKאא
א،אאאאאאאFParticlesEא
אאאאKאאאאF Laminar FlowEF٤١E،אא
אאאKאאאאאאאFTurbulent FlowEF٤١KE
F٤١Eאא F٤١Eאא
א ١٦٢ אאא אאFE א
- ٦٠ -
אאFluids in MotionW אאא،אא
KאאאאאאKאאאאSteady Uniform Flow،אא
F٤٢KEאאאFConvergentEאאאFאאF٤٢Eאא
KאאאאאFSteady Non-Uniform FlowEKאא
F٤٢אE F٤٢E
אRate of Flow
אF٤٣E،אאאאאאאאQK
F٤٣Eאאאא
א ١٦٢ אאא אאFE א
- ٦١ -
אאאאW ν ×= A Q
. νZא،AZא،Q
.Zאא אאאm3/sec
אאא⋅
m א،W
∴אZא ×א
∴ m = V × ρ
⋅
m × ρ = Q.
א15mm . 0.6 m/secאאאאאK
אW אאאW
Q. A = × ν
(0.015)2X0.6 = 106.02X10-6 m3/sec
4π = Q
.
אאאW
⋅
Q = ρ × ⋅
m
= 1000 × (106.02×10-6) = 0.106 kg/sec⋅
m
א ١٦٢ אאא אאFE א
- ٦٢ -
אאFאאE Continuity Equation אאאאFאEא
אאאאאאאאאW
= ρ1 × A1 × ν1 = ρ2 × A2 ×ν2 ⋅
m
אאאאFאא،אEContinuity EquationאLaw of Conservation of MassK
אאאKאאאאW
ρ1 = ρ2 = ρ W
A1 × ν1 = A2 × ν2
21 QQ⋅⋅
=∴ W
FConverging PipeEאF٤٤Eאאא0.46mא0.15m،אא
0.3אm3،אאאאאK
F٤٤Eא
א ١٦٢ אאא אאFE א
- ٦٣ -
אW אאW
Q.
A1 = × ν1 אאאF٤٤EK
1AQ⋅
Zν1
אאA1W
(0.462) = 166.19×10-3 m2
4π = 2
1d4π A1 =
= 1.8 m/sec 31066019.13.0
−×∴ν1 =
אאאK
17m/sec≅ = 16.98 ( )24 15.0
3.0π
= 2A
Q⋅
Zν2
אאאKאאאK
אאאאאK
A1× ν1 = A2 × ν2
224
12
14
2
11Ad
dA ×
××=
×π
π νν∴ν2 =
sec93.1615.0
8.146.02
4
24 m=
×××
π
π
∴ν2 =
א ١٦٢ אאא אאFE א
- ٦٤ -
W אאא998 kg/m3אאאא5cm
7.5cmא3.75cmאאא0.15א m3/secאF٤٥E،אW
o אאאאאאK o אאאאאאK
F٤٥Eא
אW
אאאאW
= ρ×Α1×ν1
⋅
1m
⋅⋅
×= Qm ρ1
( )sec015.09983
31m
mkgm ⎟
⎠⎞⎜
⎝⎛=∴
⋅
sec970.14 kg=⋅
∴ 1m
א ١٦٢ אאא אאFE א
- ٦٥ -
אאW .
31 2⋅⋅
×= mm
121
3
⋅⋅
×=∴ mm
sec485.797.1421
3kgm =×=
⋅
אאאW אאאאK
אA1K 22
42
141 001963.0)05.0( mdA =×=×= ππ
sec6.7001963.0
sec015.02
3
1
1
11
111
mm
mV
AQ
AQ
==
=
×=
⋅
⋅
ν
ν
אאא
אA3
sec76.6001104.0
sec0075.0
001104.0)0375.0(44
2
3
3
33
222
33
mm
m
AQ
mA d
===
=×=×=
⋅
ν
ππ
א ١٦٢ אאא אאFE א
- ٦٦ -
אאEnergy of a Liquid in Motion:
אא،אאאאאא"the capacity to do work".
،אאאאאאאאאאאאאKאא
אאא??K אאW ١E אK ٢E אK ٣E אK
אאאK
אWPotential Energy
אאאmZ Datum
LineאF٤٦KEאאאW
⎟⎠⎞
⎜⎝⎛ ×××× mmkgZgm 2sec = אPotential Energy =
אאא?א? Joule'' ''אא?J?،א
אאאאW
א ١٦٢ אאא אאFE א
- ٦٧ -
F٤٦Eאm א
⎟⎟⎠
⎞⎜⎜⎝
⎛×
kgJzg Potential Energy per Unit Mass =
אWPressure Energy
אאאKאאAאאPאא
א P)× (A אאKאאאאQ،W
ν×=⋅
AQ
אP)× (AאAQV⋅
=FKEאwork)EאאW
Work = Force × Distance
Work = p×A×ν
⋅
⋅
×=
××=
Qpwork
AQApwork
א ١٦٢ אאא אאFE א
- ٦٨ -
אא⋅
mאאאW ..
Qm ×= ρ אאאאאFEW
⎟⎠⎞⎜
⎝⎛=
×
×= ⋅
⋅
kgJp
Q
Qpρρ
work done per unit mass
אאאאאאLא،kg
J
אFאEאאא⎟⎟⎠
⎞⎜⎜⎝
⎛ρp
ρp
=א= Pressure Energy
אWKinetic Energy
אאmν،אא
FאEF ×m×ν2 ½KE W
× m × ν2 ½Kinetic Energy =
אאאאW
⎟⎟⎠
⎞⎜⎜⎝
⎛×
kgJ2
21 νZKinetic Energy Per Unit Mass
א ١٦٢ אאא אאFE א
- ٦٩ -
אאאאאא،א،אKW
אאאאZאHאHא
Per Kg = Energy Total 221 ν
ρ×++×
pzg
אאאFאאאEא
אFheight or headEW o אFPotential HeadEK o אFPressure HeadEK o אFVelocity HeadEK
אאאאאאאאאאאא
אKW
g2gpz kgPer head Total
2νρ
+×
+=
אאאאW
mm
mkgm 2
2
223
2
secsec
secmNm kgPer head Total ×+××+=
W
Total Head Per kg = m + m + m = m
א ١٦٢ אאא אאFE א
- ٧٠ -
Bernoulli Equation א?WאאאFא
אEא،אאאא?W
אHאHאK
אW
2
222
1
211
22gZpgZp
++=+ν
ρν
ρ
אאאאאאK
אאאK
F٤٧E
אאאF٤٧Eאאא
vאאhKאABCK אאA ZאאB ZאאC K
W
ccc
BBB
AAA gZpgZpgZp
++=++=++222
222 νρ
νρ
νρ
א ١٦٢ אאא אאFE א
- ٧١ -
אאאא،אאאאאA אאBאא
אK אW
אAאאBאאC אKאאW
BBB gZp++
2
2νρ
ZAAA gZp++
2
2νρ
אאאאAB
אאK אאאאאאW
energy loss between A and B +B
BBA
AA gZpgZp++=++
22
22 νρ
νρ
W
1.52 m/secאאאאאא9.14 m/secKאאא
אא15.2mKאאאאא2.339kPaKאא998 kg/m3אא993 kg/m3K؟
אW אאאW
א ١٦٢ אאא אאFE א
- ٧٢ -
112.14977.41983
0155.1344.2
2.1581.9214.9
983081.9
252.1
9981000339.2
22
2
22
2
2
22
2
21
21
1
1
++=++
×++=×++×
+=+
P
P
gZPgZP νρ
νρ
KPaP 2.184)112.14977.41155.1344.2(9832 −=−−+= אא؟K
W
אאאאאW אאאאאא
אK hsH hνZht
htאאhsאא hνאKא
אWאאאאאKאאאאאK
אאאאאאKאאאאאאW
gh
gh
2
2
2
=
=
ν
νν
W νאFm/secE
hνאFmE
א ١٦٢ אאא אאFE א
- ٧٣ -
W Kאאאאא
22אm 21.6mאאKאאK؟ אW
אאאאאאאK hν= ht - hs
hν = 22-21.6 = 0.4 m
sec8.24.081.922 mgh =××==∴ νν
אא20mmKאאא1.2kg/m3א13600kg/m3
אאאK؟ אW
אאאאW
Pν = ρ ghHg
= 13600 × 9.81 × 0.02 = 2668.32 N/m2
W
sec7.662.132.2662
2
2
2
2
m
P
P
air
air
=×=
×=
=
ν
ρν
νρ
ν
ν
א ١٦٢ אאא אאFE א
- ٧٤ -
אW אא،א
אאKאאאאאאאKאאאא
אKאאאK
Pitot Tube אKאF٤٨E
אאאאאKאאאאK
אF١EF٢EאאW
2
222
1
211
22gZ
PgZ
P++=++
νρ
νρ
אאF٢EאאאKאW
ρν
ρν
ρν
ρ
122
1221
2211
2
2
2
PP
PP
PP
−×=
−=
=+
P1אאP2 אאאאא
אK אאא
א ١٦٢ אאא אאFE א
- ٧٥ -
،אאאאאאאאאאאK
F٤٨Eא
אVenturi-MeterW
אאאא
אKאאF٤٩KEאF١EF٢EאאאK
F٤٩Eא
אאאאאאא
KאאאKאאא،אאאאאאאKא
אF١EאאF٢EאאK
א ١٦٢ אאא אאFE א
- ٧٦ -
2
22
2
21
21
1
1
22gZPgZP
++=++ν
ρν
ρ
אאאאK
ρνν
ρν
ρ
2121
22
22
221
1
1
2
2
PP
gzPP
−=
−
+=+∴
אאאW
21
21 νν ×=
AA
אאאF٢EאאW
⎟⎟⎠
⎞⎜⎜⎝
⎛−−
−=
21
22
)212
1
(2
AA
PP
ρν
١ AA2אאF١EF٢EאאK
אCo25KאאאFאאE42.1cmאאאF١E7.5cmאF٢E2.5cmאא
אאK؟ אW
אאF٢E
א ١٦٢ אאא אאFE א
- ٧٧ -
sec86.218.8988.008.8
075.0025.01
421.081.92
)1(
2
)1(
2
2
2
2
22
21
22
21
22
2
m
AA
hg
AA
===
⎟⎟⎠
⎞⎜⎜⎝
⎛−
××=∴
−
∆×=
−
∆Ρ×=
ν
ν
ρν
אאאאW
( )min
84sec
4.1001.0
sec0014.0
sec0014.086.2025.0
4 3
3
32
22litlit
litm
mmvAQ ====××=×=
⋅ π
אFאEOrifice MeterW
אא،א
אKאאאאF٤١٠EKא
KאאאאאאאאאאK
( )
⎟⎟⎠
⎞⎜⎜⎝
⎛−×
−=
21
22
212
1
2
AAPP
ρν
א ١٦٢ אאא אאFE א
- ٧٨ -
F٤١٠Eא
W
אאאאF٤١٠E0.3m/secאא0.3 mא 0.06 m،אאאאאK
אא Cv= 0.82K אW
2
1
2
2
1
2
⎟⎟⎠
⎞⎜⎜⎝
⎛−×
∆Ρ×=
AA
C
ρ
ν ν
א ν אאW
2
112 A
A×=ν
ν
אν2 = 7.5 m/sec
אאאא
KPaPaC
AA
P 739.730482
)1(
2
21
222
2
≈=×
−××=∆
ν
ρν
א ١٦٢ אאא אאFE א
- ٧٩ -
אאאW
אאאW FEאאאK FEאא1.5barא30 C0 אא
אA 400mm×300mm ،אB250mm،אאא0.2אbarAB،אאאאBא
אאאאR=287 J/kg KאאA18m/secK
אאאW אאאאאאאאא
אKאאא⋅
QאK
אא
א ١٦٢ אאא אאFE א
- ٨٠ -
אאאW Wאאאא
אאא
• אאאאאאאK
222111 vAvA ××=×× ρρ
אאFEאאW
2211 vAvA ×=×
• אאאא
אאאKאFAEאFBEאאאאK
א AאF١WE
( ) 3
5
1
1
11
725.127330287
105.1mKg
RTP
=+×
×=ρ
ρ
אBאF٢WE
( )( ) 3
5
2
2
22
495.127330287102.05.1
mKg
RTP
=+××−
=ρ
ρ
אאאאאFBEF٢E 222111 vAvA ××=×× ρρ
א ١٦٢ אאא אאFE א
- ٨١ -
אאאאv2،אאאאW
( )
( ) sec87.39
25.0495.1183.04.0725.1
222
1112
mA
vAv =×
×××=
×××
=ρ
ρ
אאאאW
אאאאK gZvPgZvP
222
111
22++=++
ρρ
אF١EF٢EאאKאאF١EאF٢EאאאאKא
אאW ( )2121
22
2ZZggZgZv
−=−= (Z1-Z2)4m،אאW
( )( )
sec86.848.92
2
2
212
mv
ZZgv
=××=
−××=
אא⋅
QW
( ) ( )
sec0695.0
sec0695.086.81.0
443
32
222
22
mQ
mvdQ
vAQ
=∴
=×=××=
×=
⋅
⋅
⋅
ππ
אאאא
אאאא
אאא المؤسسة العامة للتعليم الفني والتدريب المهني
אאאא
א
א
٥
א ١٦٢ אא אאFE אא
- ٨٢ -
אאWאאאא אאאאאK
אאW אאW
o אאאאאFאאEאאFאEK
o אאאאאK o אאא–אא
אאK o אאאK
אאאW אא٨٠٪
אאW
٦K
אאW אאא
אאW אאFאאאEK
א ١٦٢ אא אאFE אא
- ٨٣ -
W אאאאאא
FאEאאאFאEKאאאאאאKאאא
אאאא،אאאKאאא
א Surface Roughness K
אאאW אאאKא
א Pressure DropאאEnergy Head Loss،אאאאאא Friction Head K
F٥١Eאא
אאF٥١Eאא(1)א (2)אאאW
ρν×××=−
2
2
21id
lfPP
W f א،vא،ρא،lאdi א
אאK
א ١٦٢ אא אאFE אא
- ٨٤ -
אאאאN/m2K אאHW
gdlf
gPPH
if 2
221 ν
ρ××=
×−
=
אאmK
אאאW
• ⎟⎟⎠
⎞⎜⎜⎝
⎛ ××=
µρ dVRe
• אא(Relative Roughness) אאא
DεFאאE
• א(f)
F٥١Eאאאאא
)(mmDε א(Material)
0.9-9 אRiveted Steel 0.3-3 אConcrete 0.26 Cast Iron 0.15 Galvanized Iron 0.12 Asphalted Cast Iron 0.046 Commercial Steel
0.0015 Drawn Tubing Smooth FE Glass
א ١٦٢ אא אאFE אא
- ٨٥ -
Re W אאRe
µρ
ν××
=×
= HH dVdVRe
W ReZFEK VZאFm/secEK ρZאFkg/m3EK νZאאFm2/secEK µZאאFאFEN.sec/m2E
dHZאאFmEאאאאאאא،אאאאW
UAdH ×= 4
W A ZאאK UZאאK
W אאאא1mK
אW
( )( )
md
mm
md
UAd
H
H
H
1
144
414
1111114
4
2
=∴
==×
=+++
××=
×=
W
א ١٦٢ אא אאFE אא
- ٨٦ -
• 2100Re <Wא • 2100Re4000 ≥≤Wא • 4000Re >Wא
אאאאאא 2300KאF٥٢E
אאK
F٥٢אEא F٥٢Eא
Moody Diagram אאF١٩٤٤EאאאאאאאאאאFאאEאFriction
Factor Reynolds NumberאאאאW
• אאא،אW Re ≤ 2×10³
אאאאאW
Re64
=f • אאאW א 4×10³ Re ≥ א א 0.001 א
Smooth Pipe،אאW 25.0Re
316.0=f
א ١٦٢ אא אאFE אא
- ٨٧ -
• אאאאאאאאאאRough Pipe ZoneK
• אאאאאאFאאאאFεEאdE
אאTransitional ZoneאאאאאF٥٤EK
אא15m6mm
µ=0.014pa.sec2א m/sec848 kg/m³ K אW
727
014.0006.02848Re =
××=
××=
µνρ D
2100K אאW
088.072764
Re64
===f אאאאW
אF٥٣Eא
KPaPPP
vdlfPP
12.37384822
006.015088.0
22
21
2
21
=×××=∆=−
×××=− ρ
א ١٦٢ אא אאFE אא
- ٨٨ -
F٥٤EMoody Diagram
א ١٦٢ אא אאFE אא
- ٨٩ -
W אאF∆pE10mאאQ=20 l/min
3.81cmא 1030kg/m³µ= 50 ×10¯³ pa .sec אW
sec10333.3sec6002.0
min02.0min203433 mmmlQ −×====
W Q = A × V
( )
sec292.0
sec292.00381.0
4
10333.32
4
mV
mAQV
=
=×
×==∴
−
π
אW
2100Re
2.2291050
0381.0292.01030Re 3
≤
=×
××=
××= −
Q
µρ DV
אLaminar Flow
אאW
279.02.229
64Re64
2
2
==
=
=∆
f
f
VDlfP ρ
אאW
( ) KpaPaP 2.35.321510302
292.00381.010269.0
2
==×××=∆
א ١٦٢ אא אאFE אא
- ٩٠ -
W אא 3 L/secא80א˚c
52.5mm40m א80˚c971.64 Kg/m3 אאPa. sec10-3×0.358
אW
Q = 3 L/sec = 0.003 m³/sec
א
( ) sec386.10525.0
4
003.02
mAQV ===
π
Re
20000019750010358.0
0525.0386.164.971Re 3 ≈=×
××=
××=
−µρ Dv
40000،אאK
אאאK
אאε = 0.000046 m אאאW
000876.00525.0
000046.0==
Dε
אRe = 197500אא0.000876W f = 0.0208
א ١٦٢ אא אאFE אא
- ٩١ -
אW
( ) KPaP
VDLfP
8.146.971236.1
0525.0400208.0
22
2
=××=∆
×××=∆∴ ρ
אאאאאאאא
אאאאאאKאאאאא
אאאאKאCorrection FactorאאאאאאF٥٥אEF٥٥EK
אאאא50mmאאאאא450 pa/mאאאF٥٥EC801.386 m/sec.0.88
א40אm
.·. ∆p for 40m = 374 ×40 = 15 kpa
א ١٦٢ אא אאFE אא
- ٩٢ -
F٥٥אEאא0C 20
א ١٦٢ אא אאFE אא
- ٩٣ -
F٥٥EאאאאFאE
אFEאאPressure Drop in Fittings
אאאאאאאאאKא
אאאאאאK
אאאאF،T،EKKKKאאאא،א
א ١٦٢ אא אאFE אא
- ٩٤ -
אא،אאאאאאKאאאאאאFKאאE
F٥٢Eאאאאאא
א
FE
T
א
א(mm)
א
א (mm)
˚4590 ˚ 0.2 5 0.2 0.9 0.4 0.6 15.80 15 0.25 6 0.2 1.2 0.5 0.8 20.93 20 0.28 8 0.3 1.5 0.6 0.9 26.46 25 0.42 11 0.4 1.8 0.7 1.2 34.04 35 0.51 14 0.5 2.1 0.9 1.5 40.90 40 0.65 17 0.6 3.0 1.2 2.1 52.51 50 0.79 20 0.8 3.7 1.5 2.4 62.65 60 0.90 24 0.9 4.6 1.8 3.0 77.92 75 1.27 38 1.2 6.4 2.4 4.3 102.3 100 1.70 43 1.5 7.6 3.0 5.2 128.2 125 2.00 50 1.8 9.1 3.7 6.1 154.1 150
W א–אאאא75mmא
90˚אא30m،אאאאאאאsec6 L/Kא998.21 kg/m3KPa/sec 10-
3× 1.008 KאK
אW אאאאא(˚90)א= 3.0m
א= 27 m3×9 אאאא0.90 =א m
א ١٦٢ אא אאFE אא
- ٩٥ -
= 2.7 m אא= 30 m
אאL = 30 + 27 + 2.7 Lt = 59.7 m
אW
( ) sec258.1
07792.04
006.02
mAQV === π
W97071
10008.107792.0258.12.998Re 3 =
×××
=××
= −µρ Dv
אאK
אאW0006.007792.000046.0
==Dε
אFאEf = 0.0208
אW( )
KPaPaP
VDLfP
587.1212587
21.9982
258.107792.0
7.590208.0
22
2
==∆
×××=
×=∆
Q
ρ
א ١٦٢ אא אאFE אא
- ٩٦ -
אאPumps and Pumping RequirementsW אאאאאK
אאאאאאKאאאאא،אאא
אאאאKאאא( pressure head ) אא( flow rate )אאא( power )א
א ( efficiency )KאאK
אF٥٦Eאא
אF١EאF٢E–אאF٥٦WE
( ).2
222
1
211
22 frictPgZVPWgZVP∆+++=+++
ρρ
WW אJK
א ١٦٢ אא אאFE אא
- ٩٧ -
W 1100 kg/m³ 2.1 pa.sec،אאאאאא
52.51אmm50 kg/secKאא(W)K אאאא90˚אTא
אאא30 KPaK
F٥٧Eא
W
( ).2
222
1
211
22 frictPgZVPWgZVP∆+++=+++
ρρ
אאאF١Eא،אF١EF٢EאאK אאאW
( ).12
22
2 frictPgZgZVW ∆+−+= אאאאאHאאאHא
אאK אאאאW
W
11.20508.01100Re ××
=××
=vDv
µρ
א ١٦٢ אא אאFE אא
- ٩٨ -
אW
( ) sec35.0
0521.04
601100
502
mAQv =
⎟⎠⎞
⎜⎝⎛××
==π
א21006.9
6.911.2
0508.035.01100Re
>
=××
=××
=µ
ρ Dv
אfW
67.66.9
64Re64
===f
אאאW
ρ×=∆2
2VDLfP
L = 1+1+3+2+15+3+1+3+6×2.1+1×0.6 +2× 0.65
L = 29+12.6+0.6+1.3 = 43.5 m
אאאאW
∆ptot = 372.1 + 30 = 402.1 kpa
FEאW
KgJ
mKg
mN
Ptot 55.3651100
10001.402
3
2=
×=
∆ρ
א ١٦٢ אא אאFE אא
- ٩٩ -
אאאPressure Drop in Air Duct FlowW
אאאKאאאאאא
אאאאאאאאאK
אאא
W ρ×=∆
2
2VDLfP
⎟⎠⎞
⎜⎝⎛=∆ 2
21 VKP ρ
W ⎟
⎠⎞
⎜⎝⎛ ×=
DLfK
KאאאResistance Coeff. Or Press. Loss Coefficient אאFאאאאאא
אאאאאאאאאא(Dampers)א
אאEאא
fDKL
DLfK
e
e
×=∴
⎟⎠⎞
⎜⎝⎛ ×=
W אא(m)Le = Equivalent Length
אאZK אאZf
אא (m)ZD
א ١٦٢ אא אאFE אא
- ١٠٠ -
אאW אאאאאאאK
QPP ×∆= אאאאאאא،
אאאאאאאאאאאK אאאאאאא
אW • אאאFriction Loss
ρ×=∆
2
2VDLfP
• אאאאאאאאאאDynamic Press. Losses
2
2VKP ρ=∆
אאFEאW
אאאW • אאאK • אאאW
١ J אK ٢ J אאFEK ٣ J אאאאאK ٤ J אKKKKKK
אאאאאאא
אאאאאאאאK
א ١٦٢ אא אאFE אא
- ١٠١ -
אאאW
Wאאא FEאאאאK FEאא10 l/secא80C0
25.5mm40mKאא80C0801 kg/mאא80C0sec.1046.4 3 Pa−×
Wאאא אא42mאא60mmKא
א90˚א45˚אK אא0.02אא480 l/min،א
אאKFא1000kg/m³ E
א ١٦٢ אא אאFE אא
- ١٠٢ -
אאאאW
אאאאW
FEאאאאKאאאאאFאאאאEאW
ρ×=∆2
2VDLfP
FE
( ) sec62.4
0525.04
001.0102
mAQV =
×
×==
⋅
π
W 400043561
1046.40525.062.4801Re 3 >=
×××
=××
= −µρ DV
אאK אא 0.046mmFאאE
אא 000876.0
0525.0000046.0
==Dε
אאf
f = 0.025 אאW
ρ×=∆2
2VDLfP
( ) kPaPaP 8.1623.162827801
262.4
0525.040025.0
2
==×××=∆
א ١٦٢ אא אאFE אא
- ١٠٣ -
אאאאW
אאאW
אאWF1L = 0.001 m3E
( ) sec6.2
06265.04
60
001.04802
mAQV
VAQ
=⎟⎠⎞
⎜⎝⎛ ××
×==
×=⋅
π
אאW
ρ×××=∆
2
2VDLfP
PaPaP 333.77773331000
26.2
06265.094.7102.0
2
==×××=∆
L = 42+ 8 × 2.4 + 4 × 1.5 + 6×0.79 =71.94m
אאאאאאאא
אאאא
אאא المؤسسة العامة للتعليم الفني والتدريب المهني
אאאא
א
א
אא
٦
א ١٦٢ אא אאFE אאאא
- ١٠٤ -
אאWאאאK אאWאאאאא
אאאK K
אאW אאW
o אאאK o אאאאK o אאאאK o אאאאאאW Jא Jא
א Jאאאא Jא Jא Jאא Jא Jא Jא Jא
אאK o אאאאאאK o אאK
אאאW
אא٨٠٪ אאW
٥K
אאW ١ J אאאאאK ٢ J אאK
אאW א،אאאK
א ١٦٢ אא אאFE אאאא
- ١٠٥ -
W אאאאאאאאא
Kאאאאא،אאאאאFאKE
אאאאאאK אאא؟،،
אאאאאאK אאWא Jא
Jא Jאאאא Jא Jא Jאא Jא،א،א Jא
אאKאאאא،אאאK
אא،אאאא
אKאא،אאW،؟K
א،אאK
א א א א א אאאאK
א ١٦٢ אא אאFE אאאא
- ١٠٦ -
אאאאW
אאא،א،אאK אאאאאW
١ J אK ٢ J FEK ٣ J אK ٤ J אאאאK ٥ J אאFHWCFEK
80 % 250 – 275 אאא
א20 % אאאאK
אאאאאא،אאKאא
אאK אאאאאK
אא،אאאאאW ١ J אאK ٢ J אאK ٣ J אאאאK ٤ J אFאEאאK ٥ J אאאאK
אאא،אאאא
אאאאK אאאאאא
א ١٦٢ אא אאFE אאאא
- ١٠٧ -
אאK אאW
אאאאאW • אא،אאאא
Kאאאא• א،
אאK • אאאא،אאK • אא،אא
٢٠٠אאאאאK • אאאאאאא
FאאKE • א،אא
אאK • אאאאאK • ،אאא
אK אאא •
אאאאK • אאאא،אא
0.7١٠K • אאאK • אאאאאאK • אאאK • אאאא
אK • אאאאאאאאאאאK
א ١٦٢ אא אאFE אאאא
- ١٠٨ -
• אK • אאאK • אאאK • K • אK • אK • K • אאK
אאאW אאאאאאאאא
אאאKאאאWאאאא؟אK
אאאאאW • אאאא،
אאאאK • אאאאאא،
אאא،אאאאאאאאאאK
א،אאאFE،אאא،אFאEאK
אאאW
١ J אאאא אאאK
٢ J אFEW אאאא،א K
א ١٦٢ אא אאFE אאאא
- ١٠٩ -
אאK ٣ J אW
אאאאאאאKאKאא
אאאאKאאאאאאאאאא
אאKאאאאאאאK
٤ J אאאאK ٥ J אאFHWCFEW
אאKאאאK٩٠٪،אאא
אאKאF٤}٤٩}٤٨EאאאK
אאאKאאא،אאאאא
אאאאאאF٦١E
F٦١EאאאאHWCF
א ١٦٢ אא אאFE אאאא
- ١١٠ -
אאאW אאאאאא
אא،אאאאאאאאאK
אאאאאאאאאאK
אאא،אאאאאאאKאאאאאKאאאאא،אא
אאאאאאK אאאאאא،
אאאאאאאאאאאK אאאאאאא
אאאאאאאאאK
אאאאאאאF٦٢KE
א ١٦٢ אא אאFE אאאא
- ١١١ -
F٦٢Eאאאאא
F٦٢Eאאאא
אאK
W אאFSAE 50Eא170 FW Centistokes
Saybolt Universal SecondsK
Wא אאF٦٢EאFSAE 50Eא170 F،א
Wcentistokes48.0אא250 saybolt universal seconds
א ١٦٢ אא אאFE אאאא
- ١١٢ -
W אא100 F אא
אאאאאא،אW 7.5 centistokes Kאאאאא
؟א אW
אא7.5א centistokesא100 F ،אF٦٢Eאאאא
FKEROSENEKE
אאאאאW אאא،אא
אאאאאאאW
F٦١WEאאאאא א אאC0 אאFmm2/secE
אא ١٥ J٨٠ ١٠–٣٠٠ V2אא١٠–٧٠ ١٦–١٦٠ V4אא
٦٣ ١٠ J٧٠ ١٦–١٦٠
V4אא٦٣
١٠ J٧٠ ٢٥–١٦٠
S ٣٠ J٨٠ ٨}٢–٣٨٠ אWE
٣٠ J٨٠ ٨}٢–٥٠٠
אDBD ٣٠ J٨٠ ١٠ J٨٠٠
א ١٦٢ אא אאFE אאאא
- ١١٣ -
אאאW
אאאאאאאא،אאW
?אאאאאK? אאאאא
אאאאאאאאאאאא،אאא
F٦٣KE
F٦٣Eאאאאא
אאW
אאאאאאKאאא
אאאאאאאאאאאאאאK
אאאאאאאאאאאאאאאאK
א ١٦٢ אא אאFE אאאא
- ١١٤ -
אאאאאאאאK אא
Kאאאאאאאאאאאאאא
אאאאאאKאאאאאאK
אאאאאאF٦٤E
F٦٤Eאאאאאאא
אאאאא،
אאFאאEאאאאאאאאאK
א،אאאאאא א א
אאאאKאאאF٦٥E
א ١٦٢ אא אאFE אאאא
- ١١٥ -
F٦٥Eאאאאאא
אאאאאא
אאאאKאF٦٦EאאאאאK
F٦٦Eאאאאא
- ١١٦ -
אאאאאאאא
אאאא
אאא المؤسسة العامة للتعليم الفني والتدريب المهني
אאאא
א
אא
א
٧
א ١٦٢ אא אאFE אאאא
- ١١٦ -
אאWאאאאK אאW א א א א א
Kאאאאאאאאא אאW
אאW o אאאאאאאא o Wאאאאאאא Jאאא J
אאא JאאאאK o אאאאאאWאאאאאאאK
אאאW אא٨٠٪
אאW
٥K
אאW אאאאאאK
אאW אאאאFאאאEאאאFאEK
א ١٦٢ אא אאFE אאאא
- ١١٧ -
W אאאFאאEאאא
٧٨٪א٢١٪אאאאאKKאאאאאKאא
אאא،אאאאאא،אאK
??אא?אאK?אא??،א?F?אאאEאאאאK
אאאאאאWאאאאא،אאאאאK
אאאאא،אאאאאאאאאא
K אאW
W ١K אאK ٢K אאK ٣K אאK
אאאאאאאאKאאא
אאKאא،אאאאאאK
אאאאK
אאא،אאא،אא
א ١٦٢ אא אאFE אאאא
- ١١٨ -
،אKאאאKאא
K אא،אאא
אאאאאאאאK
אאאאאW
אאאאאאאאאאK
אאאאאאK
אאW אאאא،אאK
אאאW • אP K • אאTK • אאν
אאאאאאאK ١ J אאאK ٢ J אא،אW
P V = (const.) T
.constT
PV=
W P Zאא، VZא ،TZאאאFE،const.Z אאאאW
א ١٦٢ אא אאFE אאאא
- ١١٩ -
• אאZאאHאא W אאZ101KN/m2Z14.7Ibf/in2
אאW אFEאW
26
23
2
101
101
11
mNMPa
mNKPa
mNPa
=
=
=
אאW
2253
25 7.14)(761001325.1101001.0101
inIbfHgcm
mNPaKPaMPa
mNbar ==×=====
• אאאZאאאHאא W
F١Z١H٢٧٣FE K0 = 1C0 + 273 EאF١אZ١H٤٦٠FER0 = F0 + 460E 273 אאאאFKE
אאאאאאW
P V = m R T
, mV
=ν P v = R T
, nVV = P V = M R T
, MRR = P V = R T
P אאV א m א R א T אאא
א ١٦٢ אא אאFE אאאא
- ١٢٠ -
M אא n אRאא)RZ ( 8314 J/Kg mol K0
אאאאאא،אאFאאאא
אE،אאאאאאא،אאאאאK،אא
אאא،אאW
• אאFT1 = T2E אאW
.constT
PV=
, T1 = T22
22
1
11
TVP
TVP
=
2V 2P = 1V 1P W
אאאאאא،( 75.7 L ) 20 galאא20 א Ibf/in2 (137.9 kPa)،אא
אF٧١KE
F٧١Eאא
א ١٦٢ אא אאFE אאאא
- ١٢١ -
אW
2
112 V
VPP =
)377)((478)/10851.37(
)/1071.75()/101/9.137(33
3322
2 gaugeabsKPaLm
LmmKNmKNP =×
××+=
−
−
P2 = 478 kPa
אאאא137.9 kPa478 kPa
• אFP1 = P2EW אאW
.constT
PV=
, P1 = P22
22
1
11
TVP
TVP
=
12212
2
1
1 TVTVTV
TV
=→=
W א1500 in3 אאאאא،אאא
אא26.67C093.3C0 אאאאא F٧٢E،אאאאK
F٧٢Eא
א ١٦٢ אא אאFE אאאא
- ١٢٢ -
אW
12212
2
1
1 TVTVTV
TV
=→=
1
122 T
VTV =
[ ]
( )33
333
2 3.18333005127367.26
)/39.161500)(2733.93( incmC
incminCV ==⎥⎦
⎤⎢⎣
⎡+×+
= ο
ο
אאאאא1500 in3 1833.3 in3
• אFV1 = V2E אאW
.const
TPV
=
, V1 = V22
22
1
11
TVP
TVP
=
12212
2
1
1 TPTPTP
TP
=→=
W אF2000Ibf/in2EF٧٣E،
80F0 250F0،אאFPgaugeEא؟
א ١٦٢ אא אאFE אאאא
- ١٢٣ -
F٧٣Eא
אW
12212
2
1
1 TPTPTP
TP
=→=
1
212 T
TPP =
( )( )
222
2 /264946080
4602507.142000inIbf
F
FinIbf
inIbf
P =
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
+
+×⎟⎠⎞
⎜⎝⎛ +
= ο
ο
א،אאW
P2 = 2649 Ibf/in2 – 14.7 Ibf/in2 = 2634 Ibf/in2
אאאאאא2000 Ibf/in2 2634 Ibf/in2
אאאאא
אאאאאאא،אאאאא،אאא
אאאאK
א ١٦٢ אא אאFE אאאא
- ١٢٤ -
W אא1500 in3א2000 Ibf/in2 ،אא
א1000 in3אאא75F0250F0אF٧٤KEאאאאאאא؟
F٧٤Eאאא
אW
2
22
1
11
TVP
TVP
=
21
1112 VT
TVPP =
( ) ( ) ( )( ) ( ) absinIbf
inFFininIbfinIbfP 2
3
322
2 /4011100046075
4602501500/7.14/2000=⎥
⎦
⎤⎢⎣
⎡×+
+××+= ο
ο
)(/3996/7.14/4011 222
2 gaugeinIbfinLbfinIbfP =−= אאFPgaugeEאאאא1500 Ibf/in2
3996 Ibf/in2
א ١٦٢ אא אאFE אאאא
- ١٢٥ -
אאאאFSIWE
( )
⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜
⎝
⎛
××
+⎟⎟⎠
⎞⎜⎜⎝
⎛××
×⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
+
+=
−
−
3
36
3
33
3
36
3
33
22
2
1039.161000
2731211039.161500
27389.23
10113793
cmm
incmin
Ccmm
incmin
CmKN
mKN
P
ο
ο
( )( )( )
( )( ) )(5.27)(27547)(276480164.0297
3940246.0/13893
32
2 gaugeMPagaugekPaabskPamK
KmmKNp ==== ο
ο
W
אא١٣אאא٢}٧KאאאאאאאאאאאאF٢٠0E،אאא٧}٦K אאאאאאא؟אאא
אW
οKT
mVmV
barPbarP
PPP
abs
ABS
eatabs
29327320
11
5.75.6122.82.711
1
2
32
31
=+=
=
=
=+==+=
+=
אאW
2
22
1
11
TVP
TVP
=
א ١٦٢ אא אאFE אאאא
- ١٢٦ -
οο CKPTP
VPTVP
T 473205.72932.8
2
21
22
2111 ==
×===
אאאאאאאאאא
٤٧0K
אאאאW אאאאKא
אאKאאאא،אאאאאאאK
אאאאאאאK
אאאW אאאאאאאאW
• אאאFDry airEW אN٧٨٪אO2٢١٪אאאא
١٪K
• אאאFHumid airEW אאאHאאאאאאK
• אאא אאאאאאאאא
אK • אאאFTdbEW
אאאאאאאאK • אאאFTwbEW
אאאKאא،אאאKאאא
א ١٦٢ אא אאFE אאאא
- ١٢٧ -
אאאאאאאאאאKאאאאא
• אFTdpEW אאאאאאאאאK
אאאאאאאK • אW
אאאאאאאאאאKKאאאאאאאאאאא
אאאאאאאאאאאאאאאאK
אאאאאאאאאאאאK
• אאW אאאאאאאאאא
אאאאאאאK • אאW
אאאאאאאאאאאאאאK
• אאW אאאאאאאא
אאK • אאW
אאאאאאאאK
א ١٦٢ אא אאFE אאאא
- ١٢٨ -
אא( Psycrometric Tables)W אאאאאאאW
אאא،אאא،אא،אאאאאאאאאאK
א( Psycrometric Chart)W
אאאאאK
א،אא،אאאW ١ J א( Saturation Line)
F٧٥EWא،אאאא
א،אאא(t)Kאאא
(pv)FאאKE(a)F٧٥KEאאא(t) Kאא(a)אK
٢ J אאא(Constant Dry Bulb Temperature Line)W אאF٧٥EאאK
א ١٦٢ אא אאFE אאאא
- ١٢٩ -
٣ J א(Constant Humidity Ratio Lines)W אאאF٧٥Eא(H)K
٤ J אא(Constant Relative Humidity Lines)W אא،אאא(t)Kאא
אאא(R.H.= 0)א(R.H.= 1)אK
F٧٦Eאא
אאא(t)Kאא،
אא(H = C)F٧٦KE
٥ J אא(Constant Specific Enthalpy Lines) W
F٧٧Eאאאאא
א ١٦٢ אא אאFE אאאא
- ١٣٠ -
א،אאאFtKEאFHE،FaEF٧٧KEאאאFtKEאא
FaEאFi=cKEא،אאאאאFtKE
٦ J אאא(Constant Wet Bulb Temperatures)W
אאאאאא،F٧٧E،אאאKא
אFaEאאאKFaaEאF٧٧EאאאFta=cKE
٧ J אא(Constant Specific Volume Lines)
F٧٨Eאא
א،אאאFpvKE
אאFtKEFaEF٧٨KEאאאKאאFaEאאFv=cKEא
א،אאאאאK
א ١٦٢ אא אאFE אאאא
- ١٣١ -
F٧٩Eאאאא
אF٧٩EאאאאאFd.b &
w.bEFd.b & R.HEoאK א(Importance of Psychrometry)W
אאאאאאאא(Comfort
Condition)KאאאאאאאאאאF٧١٠KE
F٧١٠EFאאEא
אאא٣٠٪٣٥٪אאאא
א ١٦٢ אא אאFE אאאא
- ١٣٢ -
٢٢0٢٤0אא٤٥א٪٥٠٪אאא٢٤א0٢٦0Kאא
אאאאאאאאאאאK
אאאאאאא،אאאאא،אאKאא
אא،אאאאאK אאאאאאא
אאאאאאאK
W אאF٧١١E،אאאאא
אאאאאאאאKאאאK
F٧١١Eא
אא،אאאאאא
K
א ١٦٢ אא אאFE אאאא
- ١٣٣ -
אW אאF٧١٣EאFsEאא
אאFIEאאאK
F٧١٢Eא
אאאFdpEאאאFsE،
אאאאאK Wאאאאאאא
אאאאFאF٧١١EE،אאאFsEאאאK
- ١٣٤ -
אאאאאא
אאאא
אאא المؤسسة العامة للتعليم الفني والتدريب المهني
אאאא
אא
א
٨
א ١٦٢ אא אאFE אאא
- ١٣٤ -
אאWאאאK
אאWאאאאאאאאK
אאW אאW
o אאאאאאאאK o אאאאאK o אאאאאאK
אאאW אא١٠٠٪
אאW
٥
אאW אאאאאאאאאא
אאאאאאאK
אאW אאאאאאאאK
א ١٦٢ אא אאFE אאא
- ١٣٥ -
W אאאאאא،אאא
א،אאאאאK
אאאאW אאאאאאאK
אאאאאאW ١ J אאאK ٢ J אאאאK ٣ J אאאK ٤ J אאאאK ٥ J אאאאאאK ٦ J אאאאאאאK ٧ J אאא،אאאא
אK ٨ J אאאאאאK ٩ J אאאאאK
١٠ J אאאאK ١١ J אאאאאאK ١٢ J אאאאאK
אאאאאW ١ J אאאא ٢ J אאאאאאא،א ٣ J אFאאאE ٤ J אאאאא
אF٧EאFאאEאאאאK
א ١٦٢ אא אאFE אאא
- ١٣٦ -
٥ J אאאK ٦ J אאא،אK
אאאW אאאאאאאאאא،
אאאאאאאK א،אאאאא
אאאאאאאאאאאאאאאאאאK
אF٨١אEאF٨١EאאאאאK
F٨١אEאאא
א ١٦٢ אא אאFE אאא
- ١٣٧ -
F٨١Eאאא
אאW אאאאאאאK
אאאאW
• אW אאאאאFE
אאאאאאF٨٢E • אW
אאאאאKאאאאאאאאאF٨٣KE
אאאאאKאF٨٤EאKאאאא،
אאאאאאאאאאאK
א ١٦٢ אא אאFE אאא
- ١٣٨ -
F٨٢Eא
F٨٣Eא F٨٤Eא
אFאEW
אאאאאאאאKאאא
אאאאF٨٥KE
א ١٦٢ אא אאFE אאא
- ١٣٩ -
F٨٥Eא F٨٦Eא
אW
אא אאאאFאאEאF٨٦KE
אאW
אאאאאאאKאא،אא
אF٨٧EאאאאאK
F٨٧Eאאאא
א ١٦٢ אא אאFE אאא
- ١٤٠ -
אאW אאאאאאKא
F٨٨EאאאאK
F٨٨Eא
אאאאאאאאאאאאK
אאאאאא،אא،אאWאאאא
אאאK אאאאאא
F٨٩EK
א ١٦٢ אא אאFE אאא
- ١٤١ -
F٨٩Eאאאא
אאW
١ J אאאK ٢ J אאאK ٣ J אאאאK
א ١٦٢ אא אאFE אאא
- ١٤٢ -
אאאאW o F٨١٠EK o F٨١١EK o F٨١٢EאאאK
F٨١٠E
F٨١١E F٨١٢Eאאא
אאאאאאא،
אK
א ١٦٢ אא אאFE אאא
- ١٤٣ -
אW אF٨١٣EKאאאא
אF١EאF٢EאF٣KE
F٨١٣Eאא
א،אאאF٣KE
אאאKאאאאF٤EאF٥KEאאאאאF٦EKאא
אאK
١Kאא ٨K ٢Kאא ٩Kא ٣Kאאא
١٠Kאאא
٤K ١١K ٥Kאא
א ١٢K
٦K ١٣Kא
٧K ١٤Kא F٨١٣EאאFE
א ١٦٢ אא
אאFE
- ١٤٤ -
אא
אאא
١ J אא،Kא،١٩٨٢K ٢ J אאא،א،א،١٩٨٢K ٣ J אאא،KאאK ٤ J אאא،KKא،אאK
אאא
1. Engineering Fluid Mechanics, Roberson-Crowe.3rd Ed. 1995. 2. Fluid Power Theory and Applications, James A. Sullivan, 4th Ed. 1989
א ١٦٢ א
אאFE
א
א אKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK
אKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK אאWאאאא
KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٢ אאאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٣
אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٣ אאאאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٤
אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٥ אאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٦
אאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٠ אאWאאאא
KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١١ אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٢
אKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٢ אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٢
אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٢ אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٣
אKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٦ אאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٨
אאאאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٢٢ אאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٢٢
אאWאFאאאE KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٢٦
א ١٦٢ א
אאFE
אKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٢٦ אאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٢٧
FEאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٢٨ אאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٣٢
אKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٣٤ אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٣٦
אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٣٦ אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٣٧
אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٣٨ אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٣٨
אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٣٩ אאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٤٠
אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٤٣ אאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٤٤
אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٤٧ אאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٤٩
אאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٥٣ אאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٥٤
אאאWאFאאאE KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٥٩
אאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٥٩ אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٦٠ אKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٦٠
אאFאאEKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٦٢ אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٦٦
אKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٦٦ אKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٦٧
א ١٦٢ א
אאFE
אKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٦٨ KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٧٠
KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٧٢ אKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٧٤
אKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٧٥ אFאEKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٧٧
אאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٧٩ אאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٨٠
אאWאא KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٨٣
אאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٨٣ ReKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٨٥
KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٨٦ אFEאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٩٣
אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٩٦ אאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK٩٩
אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٠٠ אאFEאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٠٠
אאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٠١ אאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٠٢
אאWאאאא KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٠٥
אאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٠٦ אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٠٧
אאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٠٨ אאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٠٨
KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١١٠אאא
א ١٦٢ א
אאFE
אאאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١١٢ אאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١١٣
אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١١٣ אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١١٤
אאWאאאא KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١١٧
אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١١٧ אאאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١١٨
אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١١٨ אאאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١١٩
אאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٢٠ אאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٢١ אאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٢٢ אאאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٢٣
אאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٢٦ אאWאאא
KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٣٥ אאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٣٥
אאאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٣٥ אאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٣٦
אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٣٧ אFאEKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٣٨
אאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٣٩ אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٤٠
אKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٤٣ אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٤٤
אאאאאא
אאFאEא
GOTEVOT appreciates the financial support provided by BAE SYSTEMS