មេកានិកនៃសន្ទនីយ៍

CMBUkTI1 Chapter 1
I-lkVN³TUeTAGeneral
I-1-1-niymn½yrbs;vtßúravDefinition of fluid
vtßúravmancrwkeRcInya:gKÅ :
k¦ CarUbFatuEdlfitenAeRkamTMrg;Caliquid nig Solid
x¦ vtßúrav KWCarUbFatuEdlmankarERbRbYlTMrg;kñúgkrNImanGMeBIBIxageRkA .
eKehAfa karcl½trbs;PaKl¥iténvtßúrav (Particulars of fluid) .
K¦kMLaMgxageRkAGacbNþalbegþIteGaymanCaclnarbs; fluid tamTisedAénkMLaMg .
X¦eKkMNt;tamlkVN³mCÄd§anénkarxUcRTg;RTay nig mCÄd§anénkareFVIbnþ.
g¦vtßúrav KWmanrUbragdUcmCÄd§anénkareFVIbnþ EdlbgðajGMBITMrg;m:UelKulrbs;rUbFatuedayKit
bBa¢ÚlTaMgemKuN nig smIkar constitutive .
c¦ eKEckCavtßúrav nig hÁas .
]TarhN_ ³ TwkCa fluid incompressible.
hÁasCa]s½μncompressible.
CaTUeTAeKkMNt;famanBIrsarxarbs;mecanic of fluid KW
a) DINamiuc én vtßúrav b¤ Hydrodynamic.
b) DINamiuc én haÁs b¤ Aerodynamic.
q¦ TMrgrbs;vtßúravKWmaneTAtamTMrrbs;eRKOgRTehIyépÞb:HCamYybriyakasvaCaépÞesrI (Face Free).
I-1-2-niymn½yrbs;GuIRdUDINamic Hydrodynamic
- sikSaeTAelIclnarbs; vtßúrav KWCamCÄd§anénkareFVIbnþ EdlTak;TgeTAnigrMhUrrbs; vtßúrav
nigRbsiTi§PaB epSg²eTotrbs;va .
- hÁasKWsikSaGMBIrMhUr]s½μnepSg ²
- emkanic énvtßúrav nig emkanic én vtßúrWg solidmansarsMxan;epSgKña² .

emkanic én vtßúravMechanic of Fliud
emkanic én vtßúrav (EdlmanCatiTwk, ]sμ½n) emkanic énvtßú rwg
GIuRdUDINamiuc GaeGrU:DINamiuc
Hydrodynamic Aerodynamic
I-1-3-RbePTénrMhUr Type flow
k¦ rMhUrrbs; vtßúrav Caclna Continue .
x¦ cMeBaH vtßú rWg bnøas;bþÚrCabøúk .
K¦ rMhUrrbs; vtßúrav manlkVN³Cael,Ón edaykMlaMgsm<aFniglkVN³epSgeTot dUcCadg;sIuet nig
Viscosity .
X¦ Viscosity KWCargVas;er:sIusþg; én vtßúrav rbs;rMhUrehIyKWCalkVN³kkitrvag clnaPaKl¥it .
c¦ Hydrodynamic KWCa Hydrostatic KWsikSavtßúravenAhñwgmYykEnøg.
q¦ rMhUr vtßúrav Bit KWCa Laminar ( rMhUrrbs;vamanlkVN³CaRsTab;²)
C¦ cMeBaHrMhUr Turbulent CarMhUrxñÚlxñaj;.
Q¦ rMhUurÉksNñan Uniform KW g = 0 ehIyviucT½r el,Ón Velocity RsbKñaRKb;cMNuc .
j¦ rMhUurCaTUeTAmanEbkCa x , y , z EdlmaneQñaHehAfa Tridimensionnel. RbsinebIrMhUrmanEt
BIrmuxRBYj KWCarMhUr Bidimensionnel b¤ Plan. EtebImanEtmYypøÚvrMhUrenHehAfa Unidimensionnel .
I-2- c,ab;rkSaTukénkMlaMg Laws of conservation
1-kMmøaMgmanEckCaBIrKW ³
– kMmøaMgekItedayTMnajEpndI Gravitational constant (g = 9.81m/s² )
–. kMmøaMgekItedaykarkkit nig sm<aF
2- kMmøaMgenHmanTMnak;TMngCamYy cMnYnerNul Reynolds (Re) KWmankMmøaMgniclPaB nigkMmøaMg sm<aF.
3-kñúgkarGnuvtþ eKman c,ab;rkSaTukénkMlaMgsMrab;sersrGMBIclna én vtßúrav.
i) c,ab;rkSaTukénm:as;tameKalkarRKwH én Continuity
ii ) c,ab;rkSaTukénbrimaNclnatameKalkarRKwH énm:Umg;( dynamic)

iii ) c,ab;rkSaTukénfamBl( eKalkarRKwH thermodynamic )
I-3- TMhM nig xñat Dimensions&Unit
1-bNþay ( L)
2-ry³eBl ( t )
3-ma:s; ( m )
4- sIutuNðPaB ( t , ˚K )
i) kmøaMgForce in pounds = ma:s; mass in slugs ( m ) x acceleration TMnajEpndI ( g )
SI = kmøaMg ( jÚtun )
ii)  ma:smaD = = 3
m
Kg
V
M

iii) kmμnþ ( T ) =F x cMgay ( L ) =( Nm ) b¤ ( j ) hSÚl
I-4-1 Fluid Properties
1) Density
V
m
 ; 





3
m
Kg
2) Tm¶n;maD Specific Weight  g ( N/m³ ) , 





 3
m
N
V
M

3) maDykSfaRbePT Specific Volume ( SV ) ,

1
SV ; 





Kg
m3
4) dg;sIuetyfaRbePT Relative density( RD)
eau
RD


 ( Pa = 1 atm , T = 3.98 ˚C )
5) BIsáÚEm:Rt Pycnometer
eRbIsMras;KNnarkrTMng;maD V
ww 12 

1W , 2W Tm¶n;rbs;vtþúrav
1V , maDrbs;vtþúrav
6) GIuRdUEm:Rt Hydrometer
2
1
12
l
l
  (rUb a )
1 = ma:smaDEdlsÁal;
2 = ma:smaDminsÁal;
N
T
ML
2

7) GIuRCUEm:Rt Hydrometer
eRbIsMras;eKalkar d’Archimètre

មេកានិកនៃសន្ទនីយ៍

I-4-1- Viscosity of Fluid
1-KWCargVas;ersIusþg;énrMhUrrbs;Fluid
DIya:Rkaménel<ÓnrMhUr
A
dz
du
& ( 
A
F
) ;  Shear Stress
μ - Dynamic Viscosity Pas
dz
du
  ;
dYdV

  =
rStrainRateofShea
sShearStres
kñúgkrNIEdlμ = 0 or u = 0 Ca(ideal fluid );μ ≠ 0 Ca(Normal fluid).
2- Kinematic Viscosity 


 
s
m2

Dencity 1poise = 1 g / cm .s
s
m2
 Stokes (St) = 1 cm² / s
i) Viscosimetre visáÚsIuEm:Rt én bMBg;
ii) Viscosimetre rotatif visáÚsIuEm:Rt vil

3- sm<aFcMhay Vapor Pressure
krNI énqñMagEdlbitCit rYcdak;TwkTukeGayBuH eKsegáteXIjmancMhay TwkehIreLIg maneQμaH
ehAfa sm<aFcMhayTwk .
4-tg;süúgyfaRbePT Surface tension
m:UelKkulrbs;vaEdlekItmanenAkñúgTwkeRkamGMBIénkMLaMgkRnþak;skmμRKb;TisTI .
 
L
F
sigma


 ; J/m2







m
N
m2

ΔF kMLMagénPaByItEdlEtg RKb;sarFatu  
ΔL CaRkLaépÞénTwk.
5- kaBILarIet Capillilarity
KWbNþalmkBI surface tension   nigGaRs½yedayPaBsi¥tCab; ( adhésion ),kMLaMsi¥tCab;
( Cohésion ) . bMBg;EdlykmkeRbI Ø=10mm
rgr
h



 cos..2cos..2

qñaMgdutkMedA
cMhayTwk
Twk
²=2

h - kMBs;TwkeLIg ( depression )
  - Surface tension
 -mMulMgakWetting angle
dihtofliquiSpecificWe
r-kaMén bMBg;Radius of tube ( mm )
6-m:UDuleGLasIÞk ( E ) Bulk Modulus of Elasticity
v
dv
dp
E

 ( Pa ) b¤ (bar = 5
10 pa= 5
10 N/m2
)
1atm = 1.013bar = 760mmHg
dp- bMErbMrYlénsm<aF
-
v
dv
-bMErbMrYlénmaD
7-lkçN½ én Isothermal Conditions
RbsinebIsItuNðPaBefrenaHvamankarbMElgBIcMNuc 1  2 tamc,ab;hÁas
2211 vPvP  nig
2
2
2
1

 P
 efr
tamlT§plE = P
8-Isentropic Condition
kk
vPvP 2211  ,
2
1
2
1




 const ,
E= K . p
k – plepobénma:srbs;kMedA ( Cp ) efrCamYymasmaDénkMedA
9- vibtþ½n½ysm<aF Pressure disturbances KWvaTak;TgeTAnigbmøas;TIénvtþúravnigkarekIneLIgénel,Ón

EC 
 
k
k
P
P
T
T
1
1
2
1
2









sMrab;hÁas Acoustic Velocity RTgK
K
C p
..

10- sItuNðPaB Temperature
T(K) = T(o
C) +273.16 (Kelvin) ; o
R = o
F + 459.69 (Rankine)
tamTMnak;TMngrvag Temperature, Pressure, Volume, density én Constant mass of gas
( Considred Perfect or ideal ) Gnuvtþn¾tamrUbmnþ:
2
22
1
11
T
Vp
T
Vp
 ; pV = mRT ; p =  RT and
M
R
8314

Edl p = Pressure( Pa)
V = Volume (m3
)
T = Temperaturein K
m = mass of the gas in Kg
 = density of gas in Kg/m3
R = gaz constant ( J/Kg.K)
M = Relative molecular mass of the gas (no unit)
T = 200
C ;  = 13.580 Kg/m3
(Mercury)
 = 0.0838 Kg/m3
(Hydrogen)
 = 1000 Kg/m3
;(H2O)
11- mrimaNFarTwkVolume flow rate(Q;
.
V )
.
V = A.V (m3
/s = m/s x m2
);
12- Mass flow rate (
.
m )
.
m =
.
V  = v.A.  ( Kg/s = m/s x m2
x Kg/m3
)
13- Continuity equation
tConsmm outin
tan
..
 
V1 .A1. 1 = V2 .A2. 2
tConsVV outin
tan
..
 
v1 A1 = v2 A2
Fluid flow through a system

taragxñat
eQμaH nimitþsBØa xññatSI xñatRKiHSI
TMnajEpndI ( g) m/s2
ma;:s;maD ( ρ) Kg/m3
kMlaMg;TMgn;maD;PaBF¶n; ( F) N Kgm/s2
TMng;yfaRbePT ( γ) N/m3
Kg/m2
s2
sm<aF;kugRtaMg;
;PaByIt
(P;τ;E) Pa N/m2
Kg/m s2
famBl;kmnþ ( E;Work) J Nm Kgm2
/s2
GnuPaB (Hp) W J/s Kgm2
/s3
vIsáÚsIuetDINamiuc (μ) Pa.s Ns/m2
Kg/ms
vIsáÚsIuenTic (ν) m2
/S Ns/m2
Kg/ms
RkLaépÞ (S) m2
vUlUm (V) m3
elÇIn (v) m/s
cMNaM
1Kgf = 9.81 N ≈ 10N;
1tf = 9810N ≈ 10N;
1gf = 9,81.10-3
N ≈ 10mN;
1Kgf/cm2
= 98100 Pa ≈ 100 K Pa ≈ 10-1
MPa;
1Kgfm = 9,81 J ≈ 10J;
1tfm = 9810 J ≈ 10KJ;
1cv(1esH) = 735,5Wt;
1t = 1000Kg;
1l/s = 10-3
m3
/s ;
1P (poise) = 10-1
Pas;
1St (Stokes) = 10-4
m2
/s;
ρH2O t = 00
C : ρ = 999,841 Kg/m3
;
ρH2O t = 40
C : ρ = 999,973 Kg/m3
;
ρH2O t = 100
C : ρ = 999,900 Kg/m3
;
ρH2O t = 200
C : ρ = 998,203 Kg/m3
;

Chapter 2
Statique des fluides
Fluid of Statics
1-Unit pressure or pressure
k¦ RbsinebIeKmanRBIsragCaRtIekaNénTwkEdlmanmYyxñatTTwgén Twks¶b;tam TMnak;TMnggéometrique
¬FrNImaRt ¦ . dx = ds.cosθ ; dz = ds.cosθ
x¦ Tm¶n;rbs; fluid EdlbnþénRBwsKW  1.
2
dx
dz
g
K¦ sm<aF ( P ) KWCabrimaNsáaélénkmaøMgsm<aF 
F .
GaMgtg;sIuetkmøaMgsm<aF ³ P1( dz.1 ) , P 2( dx .1 ) nig P3 ( ds.1 )
X¦ lkçN½ÐlMnwgén force hydrostatique
i¦ kñúgTisedAedk P1.dz – P3.ds .conθ = 0
tamTMnak;TMngFrNImaRt P1 = P3
ii¦kñúgTisedAbBaÆr
0cos.
2
32  dsPdxPdx
dz
g Edl
gdzPP 
2
1
32 RbsinebI dz0 P2 = P3
g¦ P1 = P2 = P3 ¬sMrab; fluide au repos ¦
c¦ pdsF s b£ ds
dF
p  CaGaMgtg;sIueténsm<aFEdlman F nig RkLaépÞ S .
2- smIkarHydrostatique
k¦ CadMbUgkñúgTisedA Z , x , y
x¦ ebIsinmanbMBg;Twkminbmøas;TI kmøaMgEdlmanGMeBIeTAelImaD
i ¦ kmøaMgmaD  dsdzz 
ii¦ kmøaMgRkLaépÞ Pds nig dsdz
z
p
P 









iii¦ kmøaMglMnig én Z
  0. 







 dsdzzdsdz
z
p
ppds 
Edl 0


 z
z
p

iiii¦ eKGacsresr)an smIkarlM nwg





















0
0
0
z
p
z
y
p
y
x
p
x



b¤ 0. 

pgradf
iiiii¦
kmøaMgmaDénmaDmYyxañt + kmøaMgsm<aFénmYymaDxañt
iiiiii¦ CaviucT½rénkMlaMgmaD ( x , y , z )
g = 9,81 m/s2
iiiiiii¦ smIkar
g
z
p
y
p
x
p









0
0
iiiiiiii¦ tamsmtikmμ
k¦tamTisedA x 0


x
p
; P = Cte
x¦tamTisedA y 0


y
p
; P = Cte
K¦ g
z
p



   g
dz
dp








pgrad


f

f
























gz
y
x
f 0
0

3- bMErbMrYlbBaÄrénsm<aF
I) fluide incompressible fluide minbMENn)an
1)-    2121 zzgpp  
2)- kñúgkrNIEdlma:smaDén fluide efr
eK)an³   Ctezgp   tamlk§N³eRhVkg;
  Ctezgpp 


p efr eTAtamcm¶aybBaÄr Z ehIysm<aF P fy cuH

p famBlb:Utg;Esül ( m )
g TMnajEpndI m/ s2
g
p


bnÞúkBIeysUemRTIk vamantémøefrcMeBaH fluide repos .
4- sm<aFdac;xat , sm<aFrWLaTIv Pression absolue
-kñúgkrNIsm<asbriyakas eKehAva fa Pa rIÉCMerATwkvijKWCa Za
   1
'
1 ZZgPP aa   Et Za – Z1 = h
ghPaP '
1 CargVas;eFobCamYybøg;erehVr:g( 0.0)
suBaØakasdac;xat ( Pa = 105
Pa ) .
'
1P = Casm<aFdac;xat
-kñúgkarGnuvtþn_ ghP 1 Casm<aF rWLaTIv ( Pression refative) . ehIysm<aFdac;xat 1
'
1 PPaP 
5- Fluide Compressible ¬vtÚßravGacbMENn)an¦
Const KWvaTak;TageTA P , t0
rbs; fluide parfait .
RT
P


'
P’
= sm<aFdac;xat
R = PaBefrénsItuNðPaBrbs;hÁas Parfait

T = sItuNðPaBdac;xat
TR
p
g
dz
dp
.
'

cMeBaHvavtßúravIsotherme KWCakarERbRbYl 
xdp
d



x - emKuN compressible isotherme x = 5 . 10-10
Pa ‘
bMErbMrYlénsm<aFsMrab; liquide compressible
 rxpg
dz
d
 10

Pr = sm<aFrWLaTIvedayeFobsm<aFerehVr:gPo . 0 
6- vgVas;sm<aF Mesure de Pression
1-xñatsm<aF






 2
m
N
S
F
P b£ F = kmøaMg
S = RkLaépÞrag
cMNaM ³ 1bar = 105
Pa = 106
bayers
Pa
m
kgf
81,9
1
2

mm
m
kgf
1
1
2
 C.e
2-sm<aFbriyakas
eFobnIvUrbs;smuRT eKeXIjkMBs;)aet 760mm sm<aF P = 1.013 Pa  xül; = 1.225 kg / m³ RtUvsItuNðPaB
T = 15 0
C b£ 288 0
k
3-]bkrN_vas;sm<aFbriyakas
3
42.133
m
kn
hg  , sm<aFcMhay Pv = 0
Pression Z2 – Z1 = 760 mm C.e
attmosphérique

- Baromètre anéroide )ar:UEm:RtGaeNr:UGIut
- ]bkrN_vas;;sm<aFrWLaTIv( Pression relative )
111 hP  sm<aFrWLaTIv
11
'
1 hPP a  sm<aFdac;xat
- ma:NUEm:Rt( Manonètre)
eRbIkñúgbMBg;rag U Edlman 2 m ¬rbs;rlay ¦
2222 lhP m   sm<aFrelative
 222
'
2 lhPP ma  
P2 nig P’
2 maneRbIedayvas;
h1 nigl2 emIltamRkit
m nig 2 CacMnYnmFüménHydromèter
Pa sm<aFbriyakas
34443 . lhlPP mm  

h
1h
0P
ghP 0
l4 , l 3 , Δh ( m )
43 ,,  m Tm¶n;maDénvtßúrav
-ma:NUEm:Rtbr½dug
vide vism<aF
KWCaPaBxusKaμ énsm<aFvas;eXIj nig sm<aFbrikal ]-sm<aFvas;kñúgma:sIunbUmTwkman 0,690 bar
ehIysm<aFbriyakas xageRkAman 1,013bar dUecñH vide KW 1,013bar – 0,690 = 0.323 bar
cMNaM ³ P1 – P2 PaBxusKañésm<aF
A
F
P  ,
g
hP



 .
,
 
3
m
N
Pap
h


7- sm<aFénépÞesrI (Pression vide)
const
s
p
gz  smIkarRKwH Hydrostatique
-sm<aFdac;xatPression absolue nigsm<aFdac;xatPression Manamètreque suBaØakasPression vide .
k¦smIkarRKwH 
0
0
p
gz
s
p
gz 
10 ghP 

 zzgPP  00 
P0 – sm<FesrI Pression liber
Z0 – Z =h CeRmABnøicéncMNucNamYyla Pression d’immersion
‫٭‬ P = P0 +ρgh sm<aFGIRCUsþaTicPression Hydrostatique
1atm = 1kgf / cm2
= Patm , 100kPa b¤ 0,1 MPa
P0 = Patm = 98100 Pa
x¦ sm<aFma:NUemRTIk Pression manonétrique
Pm = P – Patm
Pm = P0 +ρgh – Patm
krN_Edl P0 = Patm eKKNnasm<aFm:aNUEm:RtRTIk
‫٭‬ Pm = ρ gh ( Pression manonétrique )
K¦edaysm<aFGIuRdUsþaTic dac;xat ( Pression hydrostatique absolue ) ticCagtémø sm<aFbriyakas
dUecñHeKehAfa vide
‫٭‬ Pv = Patm – P
P = 0 témøsm<aFsBaØakasPv = 100 kPa
tamkarGnuvtþn_sm<aFsuBaØakas EdlmandMeNalxøaMgeTAtamlkçNÐ½cMhayvtßúrav PaBEq¥t nig sItuNðPaBEdlpþl;eGay.
8- karviPaKFrNImaRt elIsmIkarRKwH én Hydrostatic
¬rUbk¦
P0=Patm ¬sm<aFbriyakas ¦; hreprentatique = kMBs;bgðaj
A – cMNucenAkñúgTwk
h=CeRmATwkKitBIépÞTwkxagelIeTAdl;cMNuc A
ghPm
g
P
h m


 ¬h –kMBs; Piézométrique ¦
vide absolue krN_Edldkykxül; begáIt)anCasuBaØakas (P0=0 ; Pv = Patm )

h = 10m ¬ KWKitBInIvU Piézométre cMhrnigbitCit ¦
cMeBaHkrN_ ³
PatmP 0 bgðajfa h
g
Pm


¬rUbx ¦
PatmP 0 bgðajfa h
g
Pv


g
P
g
PatmP
hPatmghP r

 

 0
0
hH = Charge hydrostatique = g
P
Z


9- RkahVik én sm<aF Représentation graphique de la pression
ghPP  0 Pression hydrostatique
kñúgkrN_CaeRmATwk Rtg;BIrcMNucxusKμa eKsresr ³
2
1
2
1
2
1
2
1
h
h
P
P
ghP
ghP
m
m
m
m










10- c,ab;cr én TwkkñúgepIg Loi des vases communicants
220110 hPPghP  
1
2
2
1



h
h
11-eKalkarN_c,ab; Pascal ¬ sm<aFGuIRCÚlik ¦
Principe de Pascal , Presse hydraulique
oP -sm<aFenAxageRkA EdlCaGnuKmn_én h
b
a
PP o 1

 b
a
P
P O
 1
 -muxkat; énBIsþúg EdlmanGgát;p©wt d ;  =muxkat;BIsþúg Ggát;p©wt FM


 ..
b
a
PpP o


-cMnYnbBa¢Úa b¤
2








d
D

edayKitGMBIfamBl EdlmanTMnak;TMngeTAgÉ 
2
: 






d
D
b
a
PP o
80,0 eTA 0,80 kM/lMelIkTMenIb 700.00KN .

Chapter 3
kmøaMgsm<aFénvtßúravEdlmanGMeBIelIépÞ
Force de la pression hydrostatique sur une surface plane horizontale
Hydrostatic Forces on Plane Surfaces
I- Hydrostatic Absolute Pressure (Pabs)
eKdwgfasm<aFdac;xatGIuRdUsþaTic ( Pression hydrostatique absolue ) KW
ghPatmPabs  b¤ ghPPabs  0 (Pa)
Etsm<aFenHmanGMeBIelIRkLaépÞ én)atGag (ω) dUecñHeKGacsresr)an ³
.'
absabs PP  (Pa)
eday Pabs ³ sm<aFGIuRCUsþaTicdac;xat
ω ³ RKLaépÞ)at (m2
)
 ghPP abs  0
'
edIm,IgayRsYl KWeKsresr P= ρghω
II-kmøaMgsm<aFelIRkLaépÞénbøg; Mgnitude of Resultant Hydrostatic Force
(Force de pression sur les surfaces planes à orientation arbitaire)
RKb;cMNucTMagGs;Edlsm<aFxus²Kañ KWvaCaGnuKmn_énCeRmATwklkVN³enHekItman cMeBaHbøg;bBa¢it .
ehIykar Gnuvtßn_xusKμaBIrYmbnþ xagelI . edayKitBImMulMgak α dUecñHeKGacsresr)an    dghPdPdP  0
edaybUkbBa¢ÚalkMLMagmYyEpñkeTotEdlRsbCamYyenaHKW
 ..0 cgghPPa  ; (Pa)
hcg –kMBs;TwkRtg;cMNucTIRbCMuTmøn; .
eday Po = Patm ;
dUcenH P = ρghc.g.ω Pressure gauge ¬ sm<aFm:aNUemRtIk¦

III- TIRbCMuTm¢n;énsm<aF Centre de Pression (Center of buoyancy)
Center Pressure KWCacMNuccab;énkMLMagenAEpñkkNþalénkMeNInrbs;kMLMagsm<aF elIépÞ.
lcp- RbEvgénTIRbCMusm<aFxageRkam (m)
lcg – RbEvgénTIRbCMuTm¶n; (m)
hcg – CeRmATwkRtg;TIRbCMuTm¶n; (m)
hcp –CeRmATwkRtg;TIRbCMusm<aF (m)
eKsresr P.lcp =∫ωdp.L


cg
x
cp
l
J
l
ω-RkLaépÞénbnÞH(m²)
jx – m:Um:g;niclPaBeFobnigépÞ TwkxagelI. j0 – m:Um:g;niclPaBeFobnigGkSRsb TIRbCMuTm¶n;.
 2
cgox ljj



cg
o
cgcp
l
j
ll
IV- KNnaRkahVikénkMLaMgsm<aF nig TIRbCMuTm¶n;énsm<aFelIbøg;ragctuekaNEkg Détermination graphoanalytique de
la force de pression et du centre de pression sur les surfaces rectangulaires planes
maDénDIya:Rkamsm<aF blghWéq ..
2
1

kMLaMgsm<aF bl
h
gghP cg .
2
..  
eK)anl = h kMBs;Twk (m)
b – TTwgbnÞHCBa¢Mag
V- sm<aFkMLaMg énvtßúrav elIRkLaépÞekag Hydrostatic Forces on Curved Surface.
Force de pression du liquide sur les surfaces courbes
manvtßúmYyxagABC .
BC CaRBMRbTl;.
Pz kMLMagbBaÄrEdlGMeBIelIcuHeRkamedayqøgkat;tamTIRbCMu
Tm¶n;ABC .

Pz CakMLaMgEdlbukBIeRkameLIgelItamTIRbCMuTm¶n;0
Pz 
c) Pz 
d) Pz 
`
 force de pression ragsIuLaMgKW
22
zx PPP 
CaTUeTAPx = 0 ; Py =ρghcgωy
rUbmnþTUeTAénkMLaMgsm<aF 222
zyx PPPP 
VI- viFIKNnaTwsedAénkMLaMgsm<aFEdlmanGMBIelIbnÞHva:n
b
h
gP
2
2
 ebIn CacMnYnsm<aFb¤bnÞHva:ndUecñH
b
n
gh
n
P
2
2

 b-TTwgTVarTwk
rYccMgayBIépÞTwkxagelIrhUtdl;TIRbCMuTm¶n; D KW
hlp
3
2
 b¤ 11
3
2
hlp  b¤  





 

i
ii
ihl ipi
11
3
2
  222
aah
n
i
hi 

Chapter 4
vtßúGENþtkñúgTwk
Flottement des corps dans un liquide
Stability of floating bodies
I- eKalkarN_RKwHéndMeNaldasIuEm:Rt Poussée d’ARCHIMED
eKEckrUbFatuCaBIrKW ABC EpñkxagelInig ADC EpñkxageRkam . ehIyvtßúFatuTMagenHfitenA
eRkamkMLMagbBaÄr.
eKsresr)an ³ 11 gwPz  , 22 gwPz 
EdlmanmaD AEFCB , AEFCD
tampldkcinmaD eK)an maD ABCD
  gwWWgPPP zzz   1212
dUecñH eKGacsresr P=ρgw
Neutral Stable Floating
a). G>P G =le poids d’un corps Wightof the body Tm¶n;rUbFatu
P = la poussé verticale Bouyaancy Force dMeNalénkMlaMgbBaÄr

w- maDvtßúravEdlpøas;TItamvtßúFatumaneQμaHehAfa maDénkaEv:n ( Volume Carene )
D- TIRbCMUTm¶n;énmaD . edaykMlaMgbBaÄr kat;tam D maneQμaH ehAfasg;dWkaErn
( Centre de Caréne ) .
C-TIRbCMuTm¶n; Centre of gravity .
tamlkV½NGENþt G = P = ρgw
II )- lkVN³lMnigvtßúGENþt Stabilité des corps flottants
stable lMnig Instable KμanlMnig

XøIgeXøagtic stable δ < r Instable δ >r
Stability of Partially Submerged Bodies.
α- AnglemMulMgak <150
,
D’
- cMNucEd½lGkS½bBaÄr
D’
P - xN³QIøgeXøag
M-cMNucemtas½g;RTIk ( Meta centric Height ) .
D- sg;;énkaErn
G- TIRbCMuTm¶n; .
r- kaM emtasg; (Meta centric Height) ;
б – PaBenAq¶ayBImCÄmNÐl excentricité
m-cMgayMeta centric Height m = 0,3 eTA 1,2
1)krNI r <б KμanlMnig instable . 2) б<r lMnIgstable
r = J0 / w
J0 m:Um:gniclPaB ;
w maDénkaEv:n r / б>1

Chapter 5
RbePTrMhUrénvtßúrav nig smIkarEb‘rnuyI
Type découlement du liqude et equation de Bernoulli
GIuRdUDINamiucKWsikSaGMBIclnaemkanicénvtßúrav . ehIyrMhUrrbs;clnaTwkKWvaTak;TgeTAnig ÷
1-kM / lMsm<aF nig kM/ lMkkitxagkñúg
2-kM/lMTIRbCMuTm¶n; .
rMhUrénclnaTwkmanEckecjCaBIrya:gKW ÷
k ¦rMhUrGnaciéRnþ ³ KWcariklkVNHtamcMNucnimYy²EdlrMhUrénel,Ón nigsm<aFERbRbYlGaRs½ytam
eBlevlat .
x¦ rMhUrGniéRnþ ³ KWCarMhUrEdlel,ÓnminERbRbYltameBlevla. rMhUrenHEbgEcgCaBIreTotKW
- rMhUrÉksNæan ³ el,Ón nig épÞxñat;rbs;crnþminERbRbYleTAtamRbEvgbeNþayRClg .
I.CMralGIuRCUlIk
II.CMral)atRbLay
b.rMhUrminÉksNæan³ el,ÓnnigépÞxñat;rbs;crnþéRbRbYleTAtamxñatbeNþaénRClg.
cMNaM ³ rMhUrenHERbRbYlCanic© .
c.rMhUr ³
rMhUrrbs;vtßúragmanEckCarMhUresrInigrMhUredaybnÞúk
> rMhUresrI ³ RbLay , swÞg , ERBk , bMBg;lUredayKμanbnÞúk
>rMhUrmanbnÞúk ³ TwkhUrkñúg bMBg;Edlmansm<aFCYyrujbEnþm .
* ExSéncrnþ nig)ac;éncrnþ

* carwklkVNHGIuRCUlicénxñatcrnþrbs;FarTwk nig el,ÓnmFümenAkñúgGIuRCUlicmancarwklkVNHdUcteTA ÷
 hmhbS )1
2
12)2 mhbP 
30-R kaMGIuRCUlic P
S
R 
S-épÞxñat;rMbUar
P-brimaRtesIm
-cMeBaHbMBg;vij 4
d
R ¬ d Ggát;pwt ¦
-el,ÓnmFüm  s
m
v
Q
v  Q=ω. v ( m³ s )
- sMrab;rMhUresrICael,ÓnenARtg;cMNc; 0.6 h . cab;BIépÞTwkcuHeRkam .
- sMrab;rMhUredaybnÞúkCael,ÓnenARtg;cMNuc
- 0.223 r KitCasMbkbMBg;mkdl;G½kS .

viFIedaHRsaykñúgkarKNnaRbLayTwk
RbLayragctuekaNBañy
b-)atRbLay ( m)
m-epIgeTvRbLay 

 g
tg
m
m
tg cot
11

B-TTwgrgVHénépÞTwkxagelI( m )
ω-RkLaépÞénmuxkat; ( m² )
χ- brimaRténmuxkat;esImrbs;RbLay ( m )
R-kaMGIuRCUedWRk ( m0
)
C- emKuNénbrimaNFarTwk m 0,5 s
Δ-kMBs;FaraTwksuvtþiPaB ( m )
n-PaBeRKImrbs;dIb¤TMrrbs;Twk
- rUbmnþEdlRtUvedaHRsayman ÷
  2
).1 mhbhhbmhW  (m²)
    2
1
22
1212).2 mhbmhb  (m)

W
R ).3 (m)
2
2
12 mhb
mhbh
R



R
n
C *
1
).4  eday ny 5.1 ; mRm 11.0 
( Pavlosky ) ny 3.1 ; mRm 13.0 
- 6
1
*
1
R
n
C  ( Manning )
-  RKC lg72.17  b¤ n
K
72.17
1


- 72.17
1

n
C lgR
-

gC 8 ( Darcy )
λ emKuN énDarcy . rYcvaTak;TgeTAnig
Re ( cMnYnerNul ) .
dv.
Re 
Re manEckCa ÷
+ Re cr = 2320 muxkat;ragmUl
+ Re cr = 580 muxkat;minmUl
cMeBaHrbbTwk ÷
LamIENr Re < Re cr
TYrb‘uyLg; Re > Re cr
5). B = b + 2mh (m)
RbLayrg)ara:bUl
tamsmIkar x2
= 2py ( P CatEmøénxñatRbEvg ) b¤ ( P Ca)ara:Em:Rt)a:ra:bUl)
2
1
m
p
h CMerArWLaTIv
H = h + Δ ( m )

hphBhw .2
3
4
3
2

     212ln212  P
    212ln212 N
PN
PN
Bh
R
3
2



cMeBaH B ≥ h eKyk B
RbLyrag ctþúekaNEkg
bB
hR
B
hB





 .
viFIKNnael,ÓnTwkmFüm:


Q
vvQ  . m/s
iRcv . ( Chézy ) m/s
l
hegR
v 

8
KWekItecjBIrUbmnþ g
v
d
l
hl
2
2
 
gRIv 

8
;
l
he
I 
gRIu  el,ÓnDINamiuc
viFIKNnabrimaNFarTwk Q m³ / s
Q = v.w m³/s
iRcwQ .. b¤ iRcwQ .. ( m³ / s )
Et Rcwk . dUecñH iKQ . ( m³ / s )
ikRicwwQ  .. ( m³ / s )
edIm,IeGayrMhUrTwkkñúgRbLaymanlkçN³l¥KWeKRtUvBinitüeTAelIel,ÓnTwk
v env = ≤ v mfüm ≤ v aff
AQ0.2
≤
w
Q
≤ k.Q0.1
v env - el,ÓnkkPk;
v aff - el,ÓneRcaHdac;
cMeBaH K

xSac;mFüm k = 0.45 - 0.50
xSacFM 0.5 - 0.6
fμtUc 0.6 - 0.75
fμmFüm 0.75 – 0.90
fμ 1.30 – 1.60
dIl,ayxSac; 0.53
dIGIdæmFüm 0.62
dIGidæexSay 0.52
l,aydIGideRcIn 0.58
dIGidæ 0.75 - 0.85
cMeBaH A
A = 0.33 ā W < 1.5 m / s
A = 0.44 ā W = 1.5 eTA 3.5 m/s
A = 0.55 ā W > 3.5
cMNaM - )atRbLaysMrab;eRsaceRsaB mantémøcab;BI b = 0.4 m eLIgeTA .
vIFIbgðajGMBItémøΔ ( m )
Q m³ / s < 1.0 1-10 10-30 > 30
Δ m 0.25 0.40 0.50 0.60

Chapter 6
kareRbIR)as;taragBiesssMrab;KNna)a:ra:Em:Rt
énRbLay
tameKalkarN_énelak Agroskine GaceGaymanRKwHsMrab;KNna)a:ra:Em:RténRbLay edayeFIV
karRsavRCaveTAelI)a:ra:Em:téntém R h-a ( kaMGIVRCUGIkEdlmanRbeyaCn¾) Rayon hydraulic a vantage .
dUecñHCadMbUgRtUvCMnYy F CaGnuKmn¾ .
sMrab;RbLayctuekaNBañy
i
Q
m
F .
4
1
0

sMrab;RbLayrag)a:ra:bUlIk
i
Q
F 1524.0
enAkñúgtarag TI v énAnnexe KWmanbgðajGMBItémø hydraulique A vantage edaysÁal; F, n rbs;
RbLay. KNnaplviC©aénkaredaHTwkecj
tamrUbmnþEdl)ansikSarYc KW ÷
RicwQ ..
Ricv .
eKGaceFIVkarsikSaeTACeRmATwkEdlRtUvbMeBjKW Gnuvtþn¾
tamrUbmnþ
d
h
a  a-CeRmATwkEdlbMeBj
h-CeRmATwkkñúglU
d-Ggát;pi©tbMBg;
eKdwgfa a=1.0 edaysmÁal;snÞsSn¾ 0 ¬sUnüÚ ¦
]TahrN¾ ikQ 00  ; iRCv 000  ; 0000 . RCWK 
Canic©Cakal a < 1 . edaydwgfa edIm,IeFIVkarKNnaGMBIrUbmnþxagelIKWRtUv Kal;pleFob
0Q
Q
A  nig
0v
v
B EdlTTYlxusRtUvcMeBaH brimaNFarTwk nig el,óÓnTwk .

tamrUb 8-8 )anbgðajfa A , B CaGnuKmn¾ En Q .
kñúgkrN× MaxA naMeGay a = 0.95
MaxB naMeGay a = 0.81
CaTUeTAlkVN³rbs;K CaGnuKmn¾d , n , a .
kñúgkarKNnan yktEmø0.013 ebId ≤ 600 mm .
n yktEmø0.014 ebI d > 600 mm .
cMeBaH Galerie , n RtUeRCIserIs tamtaragTI I kñúg Annexe . tEmøénko KWvapÞúyGMBIK dUecñHeKGacsresr
iRBCv .00
iAKQ 0
RCWK 000 
témønig B RtUveRCIserIstamExSekag rUb 8-8 edIm,IKNna k 0 , W 0 , C 0 , R o GacKNna .
taragbgðajGMBI K 0
el,ÓnkMNt;
v env = 0.7m/s cMeBaH d ≤ 500 mm
venv = 0.5 m/s cMeBaH d > 500mm .

I.smIkar Continuité sMrab;clnaTwkGciéRnþ
eKmanExSTwkmYyExSEdlman ÷
eK)an 332211
333
122
111
udwudwudw
udwdQ
udwdQ
udwdQ









( équodion de continuité )
Q1 = Q2 = Q = Cont
V1W1 = V2W2 = ……….. = V .W = const
1
2
2
1
w
w
v
v 
II.smIkarEb‘rnuyy‘ÍsMrab;crnþTwk parfait ( Nonvisqueux )
00 - bnÞat;eKal
Z1 , Z2 - kMBs;eFomrvaggk½STwk nig 00
ΔS1 , ΔS2 - cMgaycr
1-1 , 1’-1’, 2-2 , 2’ – 2’ , muxkat;TwkRtg;cMNuc

ds1 = u1dt
ds2 = u2dt
Le travail des forces de pression :
P1dw1u1dt – P2dw2u2dt = dQdt ( P1- P2 )
dQ = u1dw1 = u2dw2
dQ = u1dw1 = u2dw2
Le travail des forces de gravitaire = le travail par la force de gravité de la masse de liquide du
tronçon 1-1’ EdlmankMritkMBs;xus ² Kña KW dG ( Z1 – Z2 ) = g ρdw ds1 ( Z1 - Z2 )
= gρdwu1dt (Z1 – Z2 ) = gρdQdt ( Z1 - Z2 )
tamkarpøas;TIBI 1-2 EdlmancrnþTwkGciE®nþ dUecñHkM/lMefrKW
2222
2
1
2
2
2
11
2
22 u
dQdt
u
dQdt
udmudm
 
   2121
1
2
2
22
ZZdQdtgdQdt
uu
dQdt 





 
TIbBa©b;eKGacsresr)ansmIkar edayEckρdQdt RKb;GgÁTaMgBIr ÷
22
2
22
2
2
11
1
uP
gZ
up
gZ 

( Bernoulli )
b£ g
u
g
p
Z
g
p
Z
22
2
22
2
1
1 

Z1 , Z2 famBlénkMBs; ( m )
g
p
g
p

21
, famBlénsm<aF ( m )
g
u
g
u
2
,
2
2
2
2
1
famBlsIueNTic ( m )
karviPaKeTAelIssmIkarBernoulli énrMhUrGciE®nþ
g
u
g
p
Z
g
u
g
p
Z
22
2
22
2
2
11
1 

( Bernoulli nonvisqueuse )

1-ExS piézométrique
2-G½kSéncrnþTwk
l
g
p
Z
g
p
Z
I p















2
2
1
1
Ip = CMralGIuRdUlIk
edIm,Icg;el,ÓnTwk eKRtUv]bkN¾ eQμaHtibBItU Pitot
ghKu 2
III-smIkar Bernoulli sMrab;TwkFmμta ( Visqueux )
cph
g
u
g
P
Z
g
u
g
p
Z .
2
222
2
2
111
1
22





( Bernoulli )
Z 1 , Z 2 - kMBs;eFüb ( m )
α1 , α 2 – emKuNkUr:UlIs α = 1.02 eTA1.03
g
p
g
p

21
, - sMrab;famBlsm<aF ( m )
g
u
g
u
2
,
2
21
- kMhat;bg;tambeNþay ; TTwg én bMBs; ( m )

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