Assignment fluid year 3

sakklviTüal½yGnþrCati mhaviTüal½yviTüasa®sþ EpñkvisVkr
Hydraulic dwknaMedaysa®sþacarüa ³ Ebn Exm:Ura: TMB½r 1
ω
ε =
Ω
3
m
Q = εφω 2gH ,
s
Q = μω 2gH
μ = ε × φ =0.6 0.62
ε
φ
ω
H
A
ω
emKuNénrnæEdlRtUvbeB©jTwk
0.8eTA 0.9 kkitedayel,ÓnTwk
0.8eTA 0.9 muxkat;rnæbeBa©jTwk
0.8eTA 0.9 muxkMBs;Twk ;rn
0.8eTA 0.9 muxCaTUeTAeKyktMélrbs; µ = 0.6 eTA 0.9
ɛ = 0.62 eTA0.64
φ = 0.97
2
αν
2g
1
Z 2
rMhUrqøgkat;rnæ nigeRkamTVaTwk

a kMBs;TVaTwkebIk ,m
cth kMBs;Twks,Wt ,m
cth'' kMBs;Twks¶b;xageRkay ,m
cth =ε'×a
1
ct
j
a x
=
+å
emKuNel,Ón
0.95 0.97j = 
a
H
0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75
ε' 0.615 0.618 0.620 0.625 0.628 0.628 0.638 0.638 0.645 0.650 0.650 0.650 0.690 0.705
2
0
α2J
H = H + , m
2g
rUbTI1
cth cth''
H
0H
0J
cth
TVVVVVVVVVaTwk
xagmux
H
rUbTI2
taragbgðajGMBIε'
cth
H
0H
0J
a 2h
2J
2
2 g
a J
rlkTwkxageRkay
h av

B rgVHTwk ,m rUbmnþ
b )atRbLay ,m
m eCIget
H kMBs;Twk , m
N PaBeRKImrbs;TMr ,mm
DkMBs;bMrug ,m
rUbmnþTUeTA
edIm,IeGaymuxkat;RbLaymanlk<N³smRsbeKeRbIrUbmnþ
3
0 ct
mQ = φ × ε' × a × b × 2g(H -h ) ,
s
a kMBs;TVaTwkEdlebIk , m
b TTwgTVaTwk , m
ε' emKuNénpleFobkarebIkTVaTwk
H0 kMBs;Twkxagmux ,m
Hct kMBs;TwkxageRkayTVa
x Gab;sIuelanPaBkkit
n n
B
b
H
m h a´ ´ D
2
2
2
1 21
6 32
2 1
3
3 2
ω = bh + mh = (b+mh)h
P = b + 2h 1+m
ω ( b + mh )
R = =
P b+2h 1+m
1
tgθ =
m
a
m = Cotg =
h
Q = ω × J = ω × c R
1 1
= R × R × = × R × × ω
n n
1 mQ = × R × ,
sn
i
i i
i
b
β =
h

cMNaM
J > 0.5 eTA 0.6 m/s rt;kñúgRbLaykñúgkrNIEdlel,Ónrt;kñúgmanbBaðaBIrKW
J eRcaHdac; = KQ0.1
kkpk;
mmA = 0.33 , ω < 1.5
mmA = 0.44 , ω = 1.5 35
s
mmA = 0.55 , ω > 3.5
s
s

K emKuNeRcaHdac;
Q brimaNFaTwkkúñgRbLay m3
/s
W el,ÓnFøak;cuHRKab;dI mm/s
lkçx½NÐ
rMhUrqøgkat;rgVHragRtIekaN
J = AQ0.2
J kkPk < J < J eRcaHdac; ( el,Ónrt;kñúgRbLay)
Q h
P
B
b
z
32.5 mQ = 1.14h ,
s

sMKal;
H kMBs;Twk , m
D Ggát;p©itrbs;rnæ ,mm
ctω RkLaépÞrbs;vtßúravkkit ,m2
ωRkLaépÞ rnæ
EdlehAfarMhUrqøgkat;rnæ KWCaclnaTwkEdlrt;ecjtam RbehagRbeLaHhUrecjeTAeRkA edayb:HCamYy
briyakas; rWb:HCamYynwgvtßúravxøÜnÉg . ]TahrN_ GagsþúkTwk TVaTwk .l.
Hydrolic
CMBUkTI1
rMhUrrbs;vtßúravqøgkat;rnæ
c
c
atmP
H
A A
o
d
ctω
ωbriyakas;
(NUey)

eRbIsMrabépÞFM eRbIsMrabépÞtUc
3
mQ =
s
m emKuNbrimaNFaTwk
ωmuxkat;épÞTwk m2
H0 kMBs;TwklMeHogedayEpñk ,m
g = 9.81m/s2
rUbmnþ
1 rMhUrvtßúravqøgkCBa¢aMgesþIgEdlmankMBs;Twkefr
tamsmIkar Bernoulli BI AA eTA CC
2 2
o 0 0 c
P.C
P α J αJ tP
H + + = 0 + + + h
g 2g 2g 2gr
P0 sm<aFxageRkARtg; AA
P sm<aFxagkñúgRtg; CC
0J el,ÓnTwkrt;BIépÞb:HxagelImkrnrnæ ,m/s
ctJ el,Ónecjrnæ m/s
P.Ch kMhatbg; ,m
e m.p
e
R 100 0.6
R > 100000 μ = 0.60 0.62
ε = 0.62 0.64
φ = 0.97
x£  =
 

2
0 0 0
0H H + +
2
P P
g g
a J
r
-
=
2
ct
0H ( )
2g
J
a x= +S
0
3
Ω
H H Ω 4ω < 15%
ω
= 1% 5ω
mQ = μω 2gh ,
s
 ³ 
W  W ³

snμt; 1
=j
a x+S
ct 0= 2gHJ j
0Q = μω 2gH Q = μω 2gH
c
c
atm 0P = P
H
A A
o
0H ctω
ctJ

kñúgkrNIEdl
0 atm
2
0 0
0
0
0
P = P = P
α
H = H+
2g
H = H
Q
=
J
J
W
W muxkat;rbs;épÞTwkénGag
2
0
2 2
2
0
μω 2ghα Q
Q = μω 2g(H+ ) or Q =
2gΩ ω
1-μ α
Ω
cMeBaH
0
3
Ω
H H Ω 4ω < 15%
ω
= 1% 5ω
mQ = μω 2gh ,
s
 ³ 
W  W ³

eKdwgfaemKuNénkarkkitRtg;Rckecj
ε , φ Gnuvtþn_tamlkçN³
e
2gh
R , = 2ghJ
n
=
dUcenH
e m.p
e
R 100 0.6
R > 100000 μ = 0.60 0.62
ε = 0.62 0.64
x£  =
 

(emKuNrbs;el,ÓnTwk )

rUbmnþ
cth = ε' × a
a kMBs;ebIkTVaTwk ,m
ε' emKuNkkitrvagTwkCamYyTVaTwk
cth kMBs;TwkEdles,WtRtg;cMnucEdlTabCageK ,m
rMhUrqøgkat;TVaTwk
H
haJ
a
0J
a
cth
2
0
2g
aJatmP
ah J
Up Down
haJ kMBs;Twks¶b;xageRkayTVaTwk , m
a kMBs;ebIkTVaTwk , m
0J el,ÓnTwkxagmuxTVaTwk ,m
H kMBs;TwkxagmuxTVaTwk ,m
0H kMBs;TwklMeGogedayEPñk ,m
cth kMBs;TwkkkitenARtg;Rckecj,m
hz
kMBs;TwkenAEk,rTVaTwk ,m
2J el,ÓnTwkenAeRkayTVaTwk m/s
H 0H
a
ctJ
zh
2J
0J
zh haJ=
2
21
1
b
cth

cMeBaHel,ÓnTwkrt;xageRkamTVaTwk
ct 0 ctφ 2g(H -h )J =
nigbrimaNFaTwk
ct ct 0 ctQ = ω = ε'×a×b×φ 2g(H -h )ctJ´
sMKal;
b TTwgTVaTwk , m
dUcenH
3
ct 0 ct
mQ = φ × ε' × a × b 2g(H -h ) ,
s
2
0
0
ct
1
H = H ,m , φ =
2 α +Σξg
aJ
+ emKuNrbs;el,Ón
cMeBaH φ = 0.95 eTA 0.97 bRgYmmkvijeKGacsresr
ε' × φ = μ emKuNrbs;brimaNFarTwkhUreRkamTVaTwk
3
ct 0 ct
mQ = μ × a × b × 2h(H -h ) ,
s lkçN³edNUey (mincal;)
3
ct 0 ct
mQ = μ × a × b × 2h(H -h ) ,
s lkçN³NUey (mincal;eRkay)
a
H
0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75
ε' 0.615 0.618 0.620 0.622 0.625 0.628 0.630 0.638 0.645 0.650 0.660 0.675 0.690 0.705
ctha
rUbPaBebIkTVaTwk
kñúgkarGnuvtþn_ε' = 0.64
taragbgðajGMBItMél

CMBUkTI 2
rMhUrÉksNæanenAkñúgépÞTwkcMh
α
a
2
1α
2g
J
1P
gr
1Z i 
h = const
2
2α
2g
J
2P
gr
2Z
pc lh = h
L
'L
sMKal;
p lI = I CMralrbs;épÞTwk
i CMral)atRbLay
2
α
2g
J
famBlsIuenTic ,m
1 2P P
,
g gr r
famBlsMBaF ,m
1 2Z , Z famBlbU:tgEsül ,m
h kMBs;Twkefr,m
'a mMulMgak
L RbevgbeNþayRbLay
L' RbevgbeNþayRbLay ,m
p lh = h kMhatbg;tambeNþayRbLay,m

1 brimaNFaTwkefr ( Q = Const )
2 kMBs;TwkesμIKñaRKb;cMNuc h = Const efr
3 TwkeLIgcuHtamlkçN³esrI
4 )atRbLaymanCMrali > 0 , i = Sinα = Const
5 CBa¢aMRbLaymanPaBeRKImefr n = Const
6 bBaðaepSg²EdlmanGMeBIvaRtUvmin)anKit
rUbmnþGnuvtþn_
2
ω = Const ,m muxkat;RbLay
X = P = Const , m brimaNRbLay
R kaMrsμIGIuRdUlik ω
R = ,m
P
IP = IL //i CMralépÞTwkRsbCamYyCMral)atRbLay
h kMBs;TwkkñúgRbLayefrCanic© ,m
= c RiJ el,ÓnmFüm m/s
eday i = I
3
Q = ωc Ri or
mQ = k i ,
s
rUnmnþrbs;elak CHEZY
k = ωc R
C emKuNrbs;el,Ón
R kaMGIuRdUlik , m
ωmuxkat;RbLay
k emKuNbrimaNFaTwk
i = I = 1
I lkç½NÐ rMhUrÉksNæan

D
B
b
m=1.5
H
0H
BMnuHkat;AA
sMKal;
b )atRbLay ,m
B rgVHmat;RbLay ,m
D kMBs;suvtßiPaB , m (0.2 eTA 2m )
GaRs½yFaTwk 3
mQ =
s
m= 1.5 nig m=1 CaCMraleCIgeTrkñúgnigeRkAénRbLay
h kMBs;TwkkñúgRbLayRtg;muxkat;NamYy ,m
H = h + Δ ,m
A
A
m=1
m=1.5

II rUbmnþsMrab;KNnaemKuN Chezy nigemKuNénPaBeRKImrbs;RbLay
0.5y1 mC = R , (Pavlovski)
sn
n PaBeRKImrbs;RbLay
R kaMGIuRdUlik,m
y s½VyKuN
y = 2.5 n - 0.13 - 0.75 R( n-0.10)
y = 1.5 n cMeBaH R < 1m
y = 1.3 n cMeBaH R > 1m
kúñgkrNI n = 0.009 eTA 0.040  R=0.1 eTA 3m
c = 4 2g (k+lgR)
0.51 mc = + 17.72lgR ,
sn
0.51/61 m** c = R , Manning
sn
(enAelITIpSareKniymeRbICaCnCatiGg;eKøs)
2/3 1/21 m= R × i ,
sn
J
emKuNénPaBeRKImeRcInRbePT
( )
1/2N
2
i i
1
equiralent 1/2
x n
n =
x
é ù
ê ú
ê úë û
å
sMKal;
xi kMras;énPaBeRKImnimYy ,m
ni RKab;dInimYYy² ,m
rUbmnþenHbgðajGMBImuxkarRbLayragctuekaNBañaynig)ar:abUlik
Agroskine


h H
D
B
a
θ
b
sMKal;
b TTwg)atRbLay ,m
m. eCIgeTxagkñúgRbLay,m
h kMBs;TwkkñúgRbLay,m
D kMBs;suvtßiPaB,m
w RkLaépÞRbLay,m
2
ω = bh + mh = (b+mh)h
P brimaRtrbs;RbLay,m
B rgVHTwkxagelI,m
H = h´DkMBs;Twksurb,m
θ mMulMgak;rbs;RbLay a
m = cotgθ = ,m=0
h
2
2
P = b+2h 1+m or P=b+m'h
m' = 2 1+m
R kaMGIuRdUlik ,m
2
ω bh+mh
R = =
P b+m'h
edUm,IeGayrUbragRbLayctuekaNBañaymanlkçN³l¥RbesIrKWeKRtUvGnuvtþrUbm
nþ
0
2
0
m hb
β = and δ =
h b+mh
m = m' - m = 2 1+m - m
B = b + 2mh
rUbmnþ)ar:abUlik

muxkat;
Q = k i
RbEvgbrimaRtesIm
x = P 2τ(1+2τ)+ln( 2τ+ 1+2τ)
ω 2Bh
R = =
x 2PN
é ù
ê úë û
EdltMél N man
N = 2τ(1+2τ) + ln( 2τ+ 1+2τ)
kúñgkrNI
B h³
eK)an
x B
rUbmnþbgðajmuxkat;RbLayragctuekaNBñay nig)ar:abUlik
B
D
H
b

P
2 θ
h
H
A
B
x
y
rUbmnþ
x2
=2Py
P)ar:Em:Rtrbs;)ar:abUlik
H CMerATwk ,m
H = h+D ,m
B rgVHmat;elI ,m
D kMBs;bMrug ,m
h
τ-
P
CMerATwkR)akd
1
m-
2τ
CMerArbs;épÞTwk
2
ω = B×h ,m B = b ,m
P = B ,m
ω B×h
R = = = h ,m
P B

taragbgðajGMBIemKuNeCIgeTr
RbePTdI ,m m
dIdæ 1 eTA 1.25
dIl,aydIdæ 1.25 eTA 1.50
dIl,ayxSac; 1.50 eTA 1.75
dIxSac;suTæ 1.70 eTA 2.25
cMNaM
muxkat;)atRbLay b = 0.4m CatMélGb,brima ( Minivaum ) eKGacKNnatamviFImü:ageTot rbs;
RbLayeRsacRsBtamlkçx½NÐrbs;elak Ghirshkan
cMeBaHtMélDvijKWRtUvGnuvtþtamsþg;darUsSI
3
mQ
s ,mD
<1 0.25
1 eTA 10 0.4
10 eTA 30 0.5
>30 0.6
sikSaGMBIlkçx½NÐénel,ÓnTwk m,
s
J mankrNI2y:agKW J eRcaHdac; nig J kkPk; .
rUbmnþtamlkçx½NÐ
afJ J£ el,ÓneRcaHdac;
J el,ÓnFmμtarbs;TwkkñúgRbLay ,m/s
0.1
af = kQJ
K emKuNénel,ÓneRcaHdac;
3
4
h = (0.7 1.0) Q
β = 3 Q - m
B = ( 3 5 ) Q



rUbmnþbgðajGMBImuxkat;RbLayragctuekaNBñay nig)ar:abUlik
RbePTdI K
dIdæ 0.75
dIdæsuTæ 0.85
dIl,ayxSac; 0.53
dImemak 0.57 eTA 0.68
rUbmnþrbs;el,ÓnkkPk;
0.2
an = AQ ,m sJJ
A emKuNénel,ÓnmFümRKab;dIEdlFøak;cuHeTAkñúg)atRbLay
mmA = 0.33 w < 1.5
s
mmA = 0.44 w = 3.5
s
mmA = 0.55 w >3.5
s



WrYm = ( Σw tamEpñkP)/100
Q
× k = = α
τ
´k
wS el,ÓnRKab;dIepSg²Føak;cuHmm/s
Pi PaKryénRKab;epSg²
Q = k i

V < gh
1rF <
r
V > gh
F 1>
cariklkçN³rbs;RbLaycMhman 4FM²
1 Stationary
V = 0
Fr ( froud ) = 0
2 Subcritical
3 Studding ware flout
4 Super critical
Critical Flow

- Vc Velocity critical ,m/s
- H Hydraulic depth ,m
- G 9.81 m/s2
- Fr Froude umber
rMhUrminÉksNæan
eKGacniyayfarMhUrclnavtßúravkñúgRbLaycMhminÉksNæanKW
- CMral)at I i¹ CMralrbs;épÞTwk
- H CakMlBs;TwkERbRbYlenAkñúgRbLay
- CMerAekIneLIgtamTisedAénclnavtßúrav
- CMerAfycuHtamTisedApÞúyénclnavtßúrav
Vc
Fr = = 1
gh
begÁa
h
0i >
ExSekagrWm:U (l,akTwkekInrYcFøakcuH)
ExSekagedRKuy ( l,ak;TwkFøak )
a
0i > 
a) TwsedATwkRsktamCMral)at

b) i=0 TwsedATwkRsbtamCMral)at
a
0i <
c) TwsedATwkpÞúyBICMral

rUbmnþEdlRtUveRbIKW
0 0 0 0 0 0Q = ω c R i = k i
sMKal;
0 0 0 0ω , c , i , R CatMélEdlRtUv h = h0
sMrab;
1) i0 = i TisedARsb
2) i0 = i TisedARsbtMélviC¢man
3) i0 < i TisedApÞúy( KitkñúgtMéldac;xat)
eKeRbIkMNt;brimaNFaTwkQ’ tamclnaTisedATwki0 > 0 .
bB¢ak; ³ Q’CabrimaNFaTwkRtg;cMNucNamYyEdleyIgRtUvsÁal;beNþayRbLayeQñaH ( edb‘IhVicTis ) .
KMnUsbMRBYjrbs;épÞdIeRsacRsB
* muxkat; ED = F1 ,ha
* muxkat; DC = F1+F2 ,ha
* muxkat; CB = F1+F2 + F3 ,ha
* muxkat; BA = F1+F2 + F3+ F4 ,ha
RbPBTwk
4F
3F
2F
1F
D
B
C
E
2h
2h
3h
BMnuHkat;beNþaysMng;Farasa®sþ

rUbmnþEdlbB¢ak;GMBIclnaTwkKW
2
cin3
αQ B
= P = 1
gω
sMKal;
cinP )ar:aEm:RtsIueNTic
α emKuNkUrIyUlIs 1.0 eTA 1.01
Q brimaNFaTwkrt;kñúgRbLay m3
/s
bB¢ak;
Q’ CabrimaNFaTwkRtg;cMNucNamYyEdleyIgRtUvsÁal;tambeNþayRbLayeQμaH ( edb‘ÍhVicTis )
B rgVHxagelIrbs;RbLay ,m
ω RkLaépÞRtg;muxkat;tamcMnucnimYy²
snμt;cMeBaHrbbrMhUr
cinP > 1 rMhUrtUr:g;Esül ( rMhUr Turbulence ) Twktic
cinP = 1 Downtream rMhURRKITic
cinP < 1 rMhUrPøúyvIy:al ( rMhUr Laminar )TwkCn
b
B
rUbCamYyKña nigrUbelIsþaMEdrenHemIlkat;TTwg .

P CMerArbs;r)aMgxageRkay ,m
haJ kMBs;Twks¶b;xageRkaysMNg;begðór ,m
Z kMBs;eFobrvagnIvUTwkxageRkaysMNg;,m
b rgVHTwkhUr ,m
B muxkat;RbLayxagelI ,m
CMBUkTI3
rMhUrqøgkat;sMNg;begðór
sMKal;
P1 kMBs;r)aMgrbs;sMNg;begðór ,m
l’ 3 eTA 5 dgén H
0J el,ÓnTwkhUrxagmuxsMNg;begðór , m/s
S kMBs;rbs;r)aMg,m
1 cMNat;fñak;rbs;sMNgbegðór
sMNg;begðórmanEckCaeRcIny:agKW
a. sMNg;begðórmanCBa¢aMgesþIg
P
Z
h a J
1P
0J
 H
Q
V H S
l
D ow ntream
BMnuHkat;beNþaysMNg;begðór

H0H e
1P
0V
S
xül; P
avh
2
0
2
v
g
a
l = 3 5m for H
lkçx½NÐ
-S < 0.5H
-
2
0
0
αr
H = H + ,
2g
m
b. sMNg;begðórr)aMgRkas;
C. sMNg;begðórsßitkñúglkçN³Fmμta
0H H 0J
J
P
h
haJ
her
l S
2H < S < 10H
haJ
P
1P
H0H
l S
2
0
2g
aJ
2
0
2g
aJ
P
0H H
haJ
1P
Sl
0.5H < S < 2H

ctuekaNEkg ctuekaNBñay
RtIekaN rgVg;
H
P
0J
0J
d. rgVHrMHUrrbs;sMNg;begðór
e. sMNg;begðórragekag
f. rgVHsMNg;begðórRtg;
g. rgVHsMng;begðórbBaäit
H
P
P
H
H
P
0J
0H 1P
P
r
0
2g
aJ
cthl S
rlkTwkxμÜlsμaj;
r kaMrgVg;

h. rgVHsMNg;begðórLaetral;
i. rgVHsMNg;begðórxusFmμta
sMNg;begðórBhuekaN
sMNg;begðórragekag
sMNg;begðórmat;ragmUl
0J 0J
0J 0J
0J

mankarkkittic
B=b
mankarkkitxøaMg
B > b
2 cMNat;fñak; énsMNg;begðór
EdlrMhUrmanlkçN³ceg¥ót niglkçN³TUlay
3 RbePTrMhUrrbs;Twk
rUbmnþ
3/2
0Q = mb 2gH sMrab;rMhUredNUey
m emKuNbrimaNFaTwk
b rgVHsMng;begðór ,m
2
0
0
α
H = H + ,m
2g
J
TwkxagmuxsMNg;begðór ,m
33/2
n
mQ = σ mb 2gH ,
s
( sMrab;NUey )
nσ < 1
0J B b
0J
B
b
P1P
H0H
haJ
rMhUredNUey
2
0
2g
aJ
P1P
H0H
haJ
rMhUrNUey
2
0
2g
aJ

4.sMNg;begðórragctuekaNEkgRtg;lkçN³edNUeyEdlmanCBa¢aMesIþg
5. sMNg;begðórEdlmanCBa¢aMgesþIgedayragctuekaNEkg
a
b
xül;
c
0.27H
3H 0.67H
0.112H
0.22H0.15H0.003H
H
a
a
H
P
h
A
θ 1θ
b
P
H
a
B
sMrab;RtIekaN
2 3
5 mQ = 1.14H
s
sMrab;ctuekaNBañy
3 3
5 mQ = 1.86bH
s
eday b> 3H

0H H
1P
P
erh h
Sl
b
b
Bil
TVaTwk
6. sMNg;begðórEdlmanCBa¢aMgRkas;
3
0
mQ = ω × = φ × b × h 2g(H -h) ,
s
J
0
2
h= H
3
or
3
3
2 mQ = mb 2gH ,
s
( edNUey )
m = 0.35 eTA0.36
cMeBaHsMNg;begðórkñúglkçN³NUey
3
2 3
n 0
n
mQ = σ mb 2gH ,
s
b <1
7. sMNg;begðórEdlmanragCaekagCaExSekag
3
2
0Q = mb 2gH
m = 0.48 0.49
8. sMNg;BIlEdlfitenAsMNg;begðór

P
2h
2h
1Q
2Q
2h
rUbmnþ
3
2 3
0
0
0
mQ = ε m b 2gH ,
s
H
ε =1 - a
b+H
a emKuNrbs;rUbragBil
9 sMNg;begðórLaetral;
QLaetral; = mLaetral; x b x
3
2
02gH
3
m,
s
mLaetral; = 0.25 + 0.167( 2
1
2
H
-
H
cinP )
2
2
2
cin
2
P
gh
J
=
10>sMNg;begðóreFμjrNa
A=0.20
r=0.5t
A=0.11 A=0.11 A=0.06
t t t
1b
2b
b
B
n n n
B
h

3 3
2
0
3
2
0
max
mQ = mb 2gH ,
s
Q
b =
m 2gH
h
n =
(0.25 1.50)h
h kMBs;TwkFmμta ,m
maxh kMBs;TwkGtibrima ,m
n cMnYnrgVH

CMBUkTI 4
rlkTwkeRkaysMNg;begðór
I rUbPaBénsMNg;Farasa®sþ
rMhUrmanBIry:ag
- cr cinh < h and P > 1
rUr:gEsül ( Twktic )
- cr cinh > h and P < 1
PøúyrIy:al; ( TwkCn )
0J
0H H
cth
haJ
1P P
Upstream Down stream
0J0H H
cth
haJ
1P
P
Q

a
h
cth
2 3
1 2 3
ah J
resL a eL J
II TRmg;rMhUrrbs;TwkeRkaysMng;Fara®sþ
Q rlkTwkbkeRkay
Q rlkTwkrt;eTAmux
resL RbEvgrlkkeRBa¢akxøaMg ,m
a eL J RbEvgrlkmanlkçN³s¶b;bnþicmþg² ,m
RbePTénrMhUrrbs;rlkeRkaysMNg;begðór
manEckCaeRcIny:agKW
1 rMhUrrlkl¥tex©aHkrNI
'
cta = (h" - h ) or a>h'
2 rMhUrrlkTwkCn;krNI
a<h
a
cth'
h"
h'
h'
a
crh critich ahJ
eday
crh kMBs;rlkragdUcbUkstVeKa
critich kMBs;Twkrlksmrmü ,m
haJ kMBs;rlks¶b;enAeRkaysMNg; ,m

cth
haJ
clnavtßúrav
3 rMhUrrbs;rlkcal;mkeRkay ( rWm:U )
4 rMhUrCnlicenAxageRkayTVaTwk ( NUey )
5. rMhUrrbs;rlkCnlicxøaMehIyman]bsKÁ
P2 kMllaMgbukb®Ba©asTisrbs;vtßúrav
P1 kMlaMgbukRsbTisedArbs;clnavtßúrav
G TMnajrbs;vtßúravEdlmanlkçN³Ekgbøg;)atEtmantMéltUc G=0
P2 = P1 = 0 eday i = o
cth
h'' haJ
Kμan]bsKÁ
H
a=h''-h'
1P
h'' G
2P
ah J
1
1 Pr

6. rMhUrrlkCnlicxøaMgEtKμan]sKÁkñúglkçN³)atmanragCal,ak;
rUbmnþRKwHrMhUrrbs;rlkeRkaysMNg;begðóreKRtUvsÁal;smμtikmμ
egQ , h' , h'' , h eday Q brimaNFarTwk ,m3
/s
h kMBs;Twks<WtCitTVaTwk
h’’ kMBs;TwkenAbnÞab;BI hct ,m
hcg kMBs;TwkRtg;TIRbCMuTm¶n; ,m
tamkaGnuvtþn_KWRtUvsÁal;
2
cin 3
αQ
*** P = × B = 1
gω
eday ωmanmuxkat;TwkRtg;kMBs;s,Wt , m2
B rgVHTVaTwk ,m
*** kMBs;TwkrlkxageRkaysMNg;
'
cin
''
cin
h'
h" = ( 1+8P - 1 )
2
h''
h' = ( 1+8P - 1 )
2
'
cinP nig ''
cinP Ca)ar:asIuenTicxagmuxkat;rlkxageRkaysMNg;begðór
krNI
'
cin
''
cin
h" 2h' P > 3
P > 0.375
³ 
*karfykMlaMgrbs;TwkenAeRkaysMNg;begðór b¤ehAfakMhatbg;énkMlaMg
rUbmnþ
pc
(h'' - h')
h = ,m
4h'h''
kar)at;bg;famBlrbs;clnavtßúrav enAeRkaysMNg;begðórKW GaRs½yeTA nwgbMErbMrYlénkMBs;TwkxageRkay
fitenAkñúglkçN³tUrg;Esül ( J ekInxøaMg ) kMBs;Twktic b¤PøúyrIy:al;EdleGaymankarekIn b¤fyfamBlrbs;Twk .

eday
pch kMhatbg;rbs;famBlTwk ,m
h' , h'' kMBs;rlkTwkeRkaysMNg; ,m
¼ CaemKuNénkarkat;bnßyrbs;famBlkMhatbg;
*vIFIrkRbEvgrkecalenAeRkaysMNg;begðór b¤TVaTwk
1 rlkrMhUrtex©aH
resa) l = 2.5 ( 1.9h"-h' ) ,Pavloski GñkR)aCJrkeXIj
' 0.81
res cinb) l = 10.3h'( P - 1 ) Teheraussov GñkR)aCJrkeXIj
'
res cinc) l = 4h' 1+2P , Pikalow GñkR)aCJrkeXIj
res ' '
cin cin
19 30
d) l = ( 3 + - ) h"-h"Aivasian
P P
GñkR)aCJrkeXIj
tamrUbmnþ a nig e eKeRbIcMeBaH cinP >10 sMrab; d eRbIcMeBaH cin3 < P < 400rIÉRbEvgrlks¶b;vij
KWGnuvtþtamrUbmnþ
lavr = ( 2.5 eTA 3 ) lres
2 rlkrMhUrCnlic cin cinP <3 or P > 0.375
h"
haJ
'
cth
resl la cJ
a h"
crh =1.116h" haJ
a< '
cth
Ptr kMlaMgkkitrbs;TwkCamYy)at
P1-P2 kMlaMgsm<aFGIuRdUsþaric KWTwkmanclna
dUcenHCaTUeTA
'
3cin
'
ct
P "
( )
h
h
h
=
'
cinh' = h" P krNIEdl '
cinP 1.5<
'
resl =10.6h' ( P - 1 )cin

eRkaysMNg;Farasa®sþ EtgEtmanbBaðaekIteLIg nUvTæiBlrbs;rlk EdlkeRBa¢aly:agxøaMgbNþal
eGaytYsMNg;manlkçN³swkricrilehIy manlkçN³rMj½r nigenAEpñkcugxageRkaybMput éntYsMNg;manlkçN³sIueRcaH
dac; enAxag cug éntYsMNg;enaHedayclnaénvtßúravmineKarBtamlkç½NÐ ' '' ''
ct ct ct ah < h but h >> h J eTAvij .
dUcenHeyIgRtUvERbRbYlsMNg;xuslkç½NÐeTACasMNg;edayRtUvlkç½NÐeTAvijKW
''
ct ah < h J Canic© b¤ a normalh hJ £ rbs;RbLayxageRkay .
'
ct ah >> h J sMNg;manlkçN³KμanlMnwg
nwgeRcaHdac;EpñkRKwHeRkABIeRBaHkMlaMgrbs;rlkenAmanlkçN³xøaMgdUcenHRtUveFVIeGaysMNg;enHeGayman
kMralEvg rWeFIVkUnGag
4 kUnGagCYykat;bnßykMlaMgbukrbsrlkedayGnuvtþn_tameKalkarN_
''
ct a normalh < h hJ = rbs;RbLay
ah J
cth
1P
0H
H
2
0
2g
aJ
1
1 2
2 3
3
P ''
cth
''
cth
cth
P
0H H
sMNg;begðóreFVIGMBIfμlay
eCIgkarBarCMrabTwkxagmux
sMNg;eFVIGMBIebtugGaem
kMral
Gagkat;bnßykMlag
bukrlkeRkaysMNg;
kMralebtugGag bøúkfμ 4 x 6 karBareRcaHdac;
xagmuxsMNg;begðór xageRkaysMNg;begðór kMBs;Twk Normal kñúg
RbLayeRkaysMNg;begðór
normalh

2/3
01
q
H =
2nm gs
æ ö÷ç ÷ç ÷ç ÷÷çè ø
sMKal;
arP dMubøúkebtugGaem
parL RbEvgEdlRtUvdak;dMubøúk ,m
01H kMBs;Twksrub ,m
2
01
01 1
α
h =H + ,m
2g
J
01J el,ÓnTwkeRkaysMNg; ,m/s
rUbmnþ
"
par ct 1P = σh - H
2
01
1 0
α
H = H - ,m
2g
J
2/3
01
g
H =
m 2g
æ ö÷ç ÷ç ÷ç ÷÷çè ø
ns emKuNénTwkCnliceRkaydMubøúkebtug
M emKuNbrimaNFaTwk
q brimaNFaTwkrt;tamTVarTwkmYy²
3
m
,
sm
0H H
1P
P
0E
8D
haJ
basPhaJ
basH
0J
basL
bøúkTI1 bøúkTI2

lMhat;KMrU GMBIsMNg;Farasa®sþ
KMnUsbMRBYjGMBIsMNg;bBa¢ÚlTwk ¬ BMnUHkat; A – A ¦
H=2.24m
10.0265
h =2.04
0.2m
9.8265
10.5865
xagmux xageRkay
TVaTwk
eCIgeTxageRkaysMNg;
1.5m 1.5m
tYsMNg;
tYsMNg;
dgEdk
pøÚvLanebIkbr
bnÞÞÞÞÞHebtugGaem

maxQ = ε × φ × B 2gZ
edIm,IsikSaGMBiMsMNg;Farsa®sþcaM)ac;RtUvsÁas;smμtikmμ ³
-sikSaGMBIemkanicdIedIm,IrkTMhMRKwHrkCMrabTwkkñúgdIrkRbePTdIRTRKwHEdlCaersIusþg;rbs;dI ¬ ÉksaremkanicdI¦
- sikSaGMBIdæanelxa ¬tUb:Ul¦edIm,IrkkUteGay)anc,as;las;mun nigeFIVkarsagsg; . ¬ ÉksartUb:Ul ¦
- BinitüemIlÉksar nigr)aykarN¾rbs;GIuRdUlItEdlTak;Tg nigbBaðaCMrabrbs;Twk eCIgeTrRbEvg)atRbEvg
kMrslx½NÐxagelImuxkat;FarTwknigeRKÓgbgÁMúepSg²rbs;sMNg; . ¬ ÉksarGIuRdUlik ¦
dMeNaHRsayGMBIlMhat;sMNg;Farasa®sþsikSakUdTwkxagmuxsMNg;eGay)anc,as;las; .
-sikSaGMBIrUbmnþEdlRtUvykeTAGnuvtþn_
- sikSaGMBITTwgrgVHpøÚvTwkEdlhUrecj
-sikSaGMBIkMhat;bg;énclnaTwkEdlkkitCamYynigCBa¢aMgCamYy nigTVaTwknigGMBIepSg²xøHdUcCaRckcUl
nigRckecjrbs;clnaTwk
-sikSaGMBIRbEvgclnaTwkEdlmanlkçN³keRBa¢alxøaMgenAEpñkxageRkaysMNg; edIm,IecosvagkMueGayman
PaBeRcaHdac;eTAelIsac;ebtugnigEpñkxageRkamrbs;sMNg;
-TaMgenHKWsikSanUvemeronGIuRdUlIt .
tamrUbmnþRtUvykeTAeRbI
sMKal;
Q brimaNFaTwkEdlRtUvhUrecjGMBIrgVHTVaTwk
ε emKuNEdlclnaTwkrt;cUleTArkrgVHTVaTwk
emKuNel,ÓnTwkEdlRtUvrt;cUlsMNg;FarTwk
ε = 1
 0.95 

3
2
0.714
B = = 7.69m
0.4×1× 2×9.81(0.14)
7.19
7.05
5.75
5.045
5.05 5.55
P
B KWCaTTwgénrgVHpøÚvTwkhUr
g =9.81m/s
Z =Max mux– Max xageRkay
rkTTwgFarTwk B
B=8m
edayeFVIkareRbobeFobrvagbrimaNFarTwkbegðórecj
Qbegðór =0.4 x 8 x √9.81x 2 = 0.72 m3
/s
Q brimaNFarTwkbegðórcaM)ac;=- 0.714m3
/s
dUcenH
Q = 0.72m3/s > Q = 0.714m3
/s
karkMNt;sMNg;begðórrbs;eRKagsMNg;
r)aMeXOnTI2

kMNt;rkCMerAs,WtenAeBlTwkhUrecj
q brimaNFarTwk 1Éktþam2
/s
j emKuNelÓncrnþTwkrYm φ = 0.98
kMNt;rkCMerAs,WtenAeBlTwkhUrecj
q brimaNFarTwk 1 Éktþa m2
/s
φ emKuNel,ÓncrnþTwkrYm
tamkarkMnt;kñúgtarag '
cq & h edayGnuvtþn_tamrUbmnþ ¬A¦xagelIeK)an
'
ch ,(m) 0.016 0.018 0.020 0.025
 2
q m /s 0.082 0.092 0.102 0.127
tamrUbmnþ ¬A¦eyIgGacrkhc'',(m)
2 '
cq = 0.089 m /s h = 0.071
dUcenHkMBs;énPaBke®Ba¢alman
' 2
c
' 3
c
h 8q
hc'' = ( 1 + - 1 )
2 g(h )
2
''
c 3
0.017 8×(0.089)
h = ( 1 + - 1 ) = 0.299m
2 9.81(0.017)
edayeyIgkMNt;r)aMgeXOnmankMBs; h= 0.3m EdlCar)(aMgeXOnTI2 eK)an
2
g = 9.81 m/s
2
o
α
H = H +
2g

2
7.19 7.05 (0.63)
0.16
2 9.81
m
x
   
7.05 5.045
P= - = 2.005m 
' '
c o c
o
2
q = φ × h × 2g(P+H -h )
φ = 0.89 , P = 0.3 m , H = 0.05m
Q 0.714
q = = = 0.1785 m /s
B 4
' '
c o cq = φ × h × 2g(P+H +h ) (A)

 ''
c
min
k×h = 1.2×0.113=0.136
h = 0.5m
B rgVHr)aMg = 4m
TMnak;TMng '
cq & h kMNt;xageRkam
'
ch ,m 0.03 0.04 0.05 0.1 0.2
2
q ( m /s ) 0.073 0.168 0.203 0.217 0.336
tamlTæplkñúgtarageyIg)an
kMBs;ke®Ba¢al
' 2
'' c
c ' 3
c
2
3
h 8×q
h = ( 1+ - 1 ) = 0.113m
2 g×(h )
0.045 8×(0.178)
= ( 1+ - 1 ) = 0.113m
2 g×(0.045)
tamkarepÞógpÞat;
''
min ch > k × h BitCaRtwmRtUvkarkMNt;kMralx½NÐxageRkaysMNg;begðórRbEvgPaBke®Ba¢al ¬Lers ¦
'' '
c clres = 2.5 ( 1.9 h - h )
= 2.5 ( 1.9 × 0.113 - 0.045 ) = 0.424m
lres= 0.424m lres=0.5
RbEvgkUnGag ¬Lb ¦
EteyIgrk
RbEvgkMralbnþGMBIkUnGag
karkMNt;CMerAEdlsuIrUgxageRkaysMNg;
2 '
cq = 0.178 m /s h = 0.04m
bL =1.25 ×lres =1.25×0.5 =0.625m
bL =1m
'
res resL =2.5 ×L =2.5 ×0.5 =1.25m
1.2R
o
q
H =K×
V

edaykarKNnaCMralTwkxageRkamsMNg;Farsa®sþ
sMKal;
1....8 kMNt;elxerogEdlmanenAeRkamsMNg;
 sBaØaRBYjéncrnþTwk
So b RbEvgCMerARKwHEdlRtUvmanGMBICMrabTwk ,m
Tak kMras;dIEdlCaMTwk ,m
taragsþIGMBIRbEvgskmμxagesMNg;
rkRkadüg;énCMrabtamrUbmnþ
 Rkadüg;
LAB RbEvgsrubénCMrabTwkcab;BicMnuc 1 dl;cMnuc TI 8
H kMBs;EpñkmuxsMNg;¬ m ¦
Rkadüg;EdlTwkpulecjrUbmnþ
Lo / So >5.0 5.03.4 3.41.0 1.00
T skmμ 0.5Lo 2.5 So 0.8S0 0.5So 0.5 So 0.3So
8.8m
7.4m
1.2m
0.2m
1.2oS m
2.24H m 7.7865
6.9745
7.5745
10.5865
Ta
ែខ ពីេយសូវែម៉្រត
10.0265

 pul '
o
b
=
S

Assignment fluid year 3

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Assignment fluid year 3