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


- 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


- 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


- 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


- 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

×=⇒×=⎟⎟⎠

⎞⎜⎜⎝

⎛ ×=⎟⎟

⎠

⎞⎜⎜⎝

⎛××

××=⎥

⎦

⎤⎢⎣

⎡××→


- 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


- 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 =


- 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


- 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


- 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


- 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


אאאא

א

א

אא

٢


- ١٠ -

אאWאאאאK

אאW אאW

o אאאא o אאאאאאא

אאK

אאאW אא٩٠٪

אאW

٣

אאW אאאאאK

אאW

א،אאאK


- ١١ -

W אאאאאאאא

אאאאאאKאאאאאאאאאאאאאאK

אאאאאKאאW • אאWאאאאאK • אאWאאאאK

אאאאא

אאאאאאאאאאאאאא

אKאאאאאאאאאאאאאאאאא

אאKאא،אאאאאא،א،אאKא

אא،אאאאאK אאאאאא

אאאאאKאאאאאאK


- 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

==


- 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


- 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


- 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


- ١٦ -

אאאאאאאאW

8.01000800

===w

ffSG

ρρ

אViscosityW אא،א

KאKאאאKאאא،אאאאאאK

אאKאאאאK

אאאאאאK

F٢١Eא

אאFF٢١EEא

UאאyאAאאאFK


- 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


- ١٨ -

אאאאאאאאאאKאאא

אאאKאאאאאאK

אאאW

אאאKאאאאאאאאאאא

אאאKאא،אאאאאא

אאאאF٢ J٢KE

F٢ J٢Eאאאאאא

אF٢٣אEאF٢٣Eאאאאא

אאאKאK


- ١٩ -

F٢ J٣ JEאאאאאא


- ٢٠ -

F٢ J٣ JEאאFאEאאאא


- ٢١ -

F٢ J٤WE א אאא،א

sec1100=

dYdu1א

אא10-3 pa.secK אW

Padydu

1.010010 3 =×=∴

×=

−τ

µτ


- 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


- 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


- 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


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


- 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


- ٢٧ -

2

4dA π

=

barKPaPmKNP

P

AFP

09.5509

509

10504

1000

2

62

==

=

××=∴

=

−π

١_٣١_٣

אאאאW

אאאאאאאא،אאאא

אאאKאאFaEאאFbEאאאFcEאאFdEF٣٢EK


- ٢٨ -

אF٣ J٢Eאאאא

FEאPressure HeadW אאאאאאאאאK

אאאאאאאK אאאאאאאK

٣٣א

אאאאאאF٣٣EFρE

אאאFFEאFmEאFgEאאאFpEאW

hgP ××= ρ ( )hgp ∆××=∆ ρ

אאאh


- 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


- 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


- 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


- 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


- 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


- ٣٤ -

אFPressure MeasurementE א،אאא

אKאW

אFThe BarometerE

F٣٦Eא

אאאא،אF٣٦Eא

،א،אאאFpEאאאאא

אאאKאאאאאאאאאאאאא

אאאאאאאאאאאאאאK

א hאא ρא،אאW

P = ρ × g× h


- 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


- ٣٦ -

אאThe Manometers )E : אאאאאאK א

UאאאאאאKKאאא

KאאאאאKאאאאאאאK

אאW

אF٣٧EאKUאאאאאאאאF٣٧KE

BאCK אBאאאאאhK

אCאאאאK

PB = PC = P0 + ρHg g h

F٣٧Eאא


- 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


- ٣٨ -

אאWInclined Manometer אאאאאKא

אKאאאhX Sinθ XאאאθאאאF٣٩EK

P1- P2 = ρg X Sinθ

F٣٩Eאא

אאFאאאEW

אאאאPKאאאא،אאאאK

אאאאאאKאPאאhאאρא

אgK אאאאאאW

P = h . ρ .g


- ٣٩ -

F٣١٠Eאאאאא

אאאאאאא،א

אאאאאאF٣١٠KE

P1 = P2 = P3

אאאKאאאאאFA1 = A2 = A3Eאאאאא

FF1 = F2 = F3KE

אאFE F AF٣١١E،

P אאאאא،אK

AFP =


- ٤٠ -

F٣١١Eאא

אא،אאאאKאאא

KאאK،אאאאאאK

אאאאאאא،אאאאא،אאא

אKא،אאאא10 m א1 bar K

אאאW אאא،א،אאK

F٣١٢אEאאאאאK

F٣١٢אEאאא


- ٤١ -

אF٣١٢EאאאאאאW

F٣١٢EאFEאא

אF1אא A1 P،W

1

1

AFP =

אPאא،אA2KאF2FאאאKE

2

2

1

1

22 .

AF

AF

APF

=

=

W

1

2

1

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AA

FF

=

אאKאאאאKאאאאאא


- ٤٢ -

K אא،אF1אA1 ،אאא

אF2FאA2E،אאFאאאאKE

W אא

1

2

2

1

AA

SS

=

אאא،W

W1 = F1 × S1 W2 = F2 × S2


- 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


- 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


- ٤٥ -

KאאאK

אאF٣١٥KE

F٣١٥Eאא

אאא،אא،אW

• FאאEK • FאאEK • אFאאאEK

א FאE אאF אא K Eא אאK

אאאאאאאKאאאא،אאK


- ٤٦ -

אאאאאאK אאאאאאאאאאאK

אאאאK

אאאאאK

אF٣١٦Eאאאאא

F٣١٦Eאאאא


- ٤٧ -

אאW אאא،

א K אאא،אאPאK

אאKאאאאאK

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אאאQ،אאdF1 אP1KאאאאאW

baQF ×=1

QאאאאK אאP1אאF1 W


- ٤٨ -

21

2

1

1

11

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d

FAFP

××

=⎟⎠⎞

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==ππ

P1 = P2 = P

א א א א א

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ξאאW

80.085.0 ≥≥ ξ


- ٤٩ -

אאאאW אאאאאאאא

אאאK

F٣١٨Eאאא

F٣١٩Eאא


- ٥٠ -

F٣٢٠Eאאא

F٣٢١Eאאאאא


- ٥١ -

F٣٢٢Eאאאאאא

F٣٢٣Eאאאא

F٣٢٤Eאאאא


- ٥٢ -

F٣٢٥Eאא


- 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؟

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א؟אאא

אאאW אאא750 kg/m³10³kg/m³K

אא3mא2m،אאאאאאא אאKאאא1barK

אאא


- ٥٤ -

אאאאW אאאאא،אF א100 N

אא،אF2א؟אאאא

אאאא

אאאW

אאאאW FE

• אאאK • אאאאHאאK

FE אאאW

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אאW ( )

KPaPaP

mDrA

1358135808004418.06000

004418.0075.044

2222

≈==∴

=×==×=πππ


- ٥٥ -

FE

אאאFE

אאאאאאאאאאאאא

אאאW

KPaPaP

hgPPPP OiltopOiltop

7.10881088704)5.781.91206(1000000

)(

==××+=

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p אאאK

FE אאאאHאא

KPaPPP atmgbs 24595150\ =+=+=

אאאאW

mh

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34.1081.999910325.101

81.9999325.1013

=××

=∴

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אאאFא13600 kg/m³E

7.5 m Oil


- ٥٦ -

hhgp

××=×

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81.91360010325.101 3

ρ

h = 0.76 m = 76 cm אאא١٠٧٦K

אאאאW

אאאW

( ) ( ) kPaPaP

PPP

gage

WOilgage

5.44500100037502 ==×+×=

+=

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kPaPkPaPabarP

kPaPaP

PPP

t

atm

gage

atmgaget

5.1041005.41001000001

5.44500

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==

+=

אאאאאW

אאF1FאאאאאEאאC

אאאאW

(0.33m)(100 N) – (0.03m) F1 = 0

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10033.01 =

×=

אאאאאW


- ٥٧ -

1

2

1

2

AA

FF

=

P1 = P2 = P = F1/A1 =F2/A2

F1= P1A1= 1100 N

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26

211 1022.6

4

11001100mN

dAP ×=== π

P1= P2

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( ) kNmmNF 22.1205.0

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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

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אאW

٦K

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אאW

אאאFאאאEאאאאK


- ٥٩ -

W אאאאאאאאאאאK

אאאאאאאאאאא،א

אאאאאאאK

אאאאTypes of Fluid Flow

אאאאאאאאאאאאKאא

א،אאאאאאאFParticlesEא

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אאאKאאאאאאאFTurbulent FlowEF٤١KE

F٤١Eאא F٤١Eאא


- ٦٠ -

אאFluids in MotionW אאא،אא

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F٤٢אE F٤٢E

אRate of Flow

אF٤٣E،אאאאאאאאQK

F٤٣Eאאאא


- ٦١ -

אאאאW ν ×= A Q

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⋅

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.

אאאW

⋅

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m

= 1000 × (106.02×10-6) = 0.106 kg/sec⋅

m


- ٦٢ -

אאFאאE Continuity Equation אאאאFאEא

אאאאאאאאאW

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m

אאאאFאא،אEContinuity EquationאLaw of Conservation of MassK

אאאKאאאאW

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21 QQ⋅⋅

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FConverging PipeEאF٤٤Eאאא0.46mא0.15m،אא

0.3אm3،אאאאאK

F٤٤Eא


- ٦٣ -

אW אאW

Q.

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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

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×××

π

π

∴ν2 =


- ٦٤ -

W אאא998 kg/m3אאאא5cm

7.5cmא3.75cmאאא0.15א m3/secאF٤٥E،אW

o אאאאאאK o אאאאאאK

F٤٥Eא

אW

אאאאW

= ρ×Α1×ν1

⋅

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( )sec015.09983

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⎠⎞⎜

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⋅

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∴ 1m


- ٦٥ -

אאW .

31 2⋅⋅

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121

3

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1

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111

mm

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AQ

==

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⋅

⋅

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sec76.6001104.0

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3

33

222

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mm

m

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mA d

===

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⋅

ν

ππ


- ٦٦ -

אאEnergy of a Liquid in Motion:

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- ٦٨ -

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- ٦٩ -

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- ٧٠ -

Bernoulli Equation א?WאאאFא

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222 νρ

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- ٧١ -

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energy loss between A and B +B

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אW אאאW


- ٧٢ -

112.14977.41983

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22

2

22

2

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++=++

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hνאFmE


- ٧٣ -

W Kאאאאא

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air

air

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- ٧٤ -

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- ٧٦ -

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2

22

495.127330287102.05.1

mKg

RTP

=+××−

=ρ

ρ

אאאאאFBEF٢E 222111 vAvA ××=×× ρρ


- 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


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


- 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


- 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


- 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


- 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


- 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


- ٨٨ -

F٥٤EMoody Diagram


- 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

==×××=∆


- 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


- 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


- ٩٢ -

F٥٥אEאא0C 20


- ٩٣ -

F٥٥EאאאאFאE

אFEאאPressure Drop in Fittings

אאאאאאאאאKא

אאאאאאK

אאאאF،T،EKKKKאאאא،א


- 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


- 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


- 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


- 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


- 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


- 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


- 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


- 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


- 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

==×××=∆


- 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


אאאא

א

א

אא

٦


- 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


- 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


- 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


- 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


- 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


- ١٠٩ -

אאK ٣ J אW

אאאאאאאKאKאא

אאאאKאאאאאאאאאא

אאKאאאאאאאK

٤ J אאאאK ٥ J אאFHWCFEW

אאKאאאK٩٠٪،אאא

אאKאF٤}٤٩}٤٨EאאאK

אאאKאאא،אאאאא

אאאאאאF٦١E

F٦١EאאאאHWCF


- ١١٠ -

אאאW אאאאאא

אא،אאאאאאאאאK

אאאאאאאאאאK

אאא،אאאאאאאKאאאאאKאאאאא،אא

אאאאאאK אאאאאא،

אאאאאאאאאאאK אאאאאאא

אאאאאאאאאK

אאאאאאאF٦٢KE


- ١١١ -

F٦٢Eאאאאא

F٦٢Eאאאא

אאK

W אאFSAE 50Eא170 FW Centistokes

Saybolt Universal SecondsK

Wא אאF٦٢EאFSAE 50Eא170 F،א

Wcentistokes48.0אא250 saybolt universal seconds


- 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


- ١١٣ -

אאאW

אאאאאאאא،אאW

?אאאאאK? אאאאא

אאאאאאאאאאאא،אאא

F٦٣KE

F٦٣Eאאאאא

אאW

אאאאאאKאאא


אאאאאאאאאאאאאאאאK


- ١١٤ -

אאאאאאאאK אא

Kאאאאאאאאאאאאאא

אאאאאאKאאאאאאK

אאאאאאF٦٤E

F٦٤Eאאאאאאא

אאאאא،

אאFאאEאאאאאאאאאK

א،אאאאאא א א

אאאאKאאאF٦٥E


- ١١٥ -

F٦٥Eאאאאאא

אאאאאא

אאאאKאF٦٦EאאאאאK

F٦٦Eאאאאא

- ١١٦ -

אאאאאאאא

אאאא


אאאא

א

אא

א

٧


- 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


- 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


- 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


- 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


- 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


- 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


- 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

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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

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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

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אאאאאא

אאFאEא

GOTEVOT appreciates the financial support provided by BAE SYSTEMS

Documents

أساسيات قدرة الموائع