4.gradually varid flow part 2.pdf sjjbndnnnnjj

Open channel

1. Classification of Flow Surface
Profiles
FitsumeT.

2. Classification of Flow Surface Profiles
•Bottomslopesareclassifiedassustaining(S
o>0)andnon-
sustainingslopes(S
o≤0).
Sustainingslopes
Non sustaining slopes
Mild slope (Y
o>Y
C)
critical slope (Y
o=Y
C)
steep slope (Y
o<Y
C)
Horizontal slope (S
O=0)
Adverse slope (S
O < 0)

4. Sustaining slopes(Y
o>Y
c)
M
Zone 3 (yo>yc>y)
Zone 2 (yo>y>yc)
Zone 1 (y>yo>yc)
CDL
NDL
Yc
Y
o
E
S=Y+V
2
/2g

5. Sustaining slopes(Y
o<Y
c)
S
Zone 3
(yc>yo>y)
Zone 2
(yc>y>yo)
Zone 1 (y>yc>yo)
NDL
CDLY
C
Y
o
E
S=Y+V
2
/2g

6. Sustaining slopes(Y
n=Y
c)
C
Zone 3
(yo=yc>y)
Zone 1
(y>yc=yo)
NDL
CDLY
C
Y
n
E
S=Y+V
2
/2g

7. Non Sustaining slopes(S
o=0)
H
Zone 3
(y<yc)
Zone 2
(y>yc)
CDL
Y
c

8. Non Sustaining slopes(S
o=0)
A
Zone 3
(y<yc)
Zone 2
(y>yc)
CDL
Y
c

9. •Depending upon the channel category and region of
flow, the water surface profiles will have
characteristics shapes. Whether a given GVF profile
will have an increasing or decreasing water depth in
the direction of flow will depend upon the term
dy/dxbeing positive (back water curve) or
negative(drawdown curve).

10. y = Non-uniform flow depth.

11. y
0= Uniform flow depth,
y
c= Critical flow depth,
y = Non-uniform flow depth

12. 1.The water surface approaches the normal depth asymptotically
2.The water surface meets the critical depth line vertically.
3.The water surface meets a very large depth as a horizontal
asymptote

13. Based on this information, the various possible gradually
varied flow profiles are grouped into twelve types
Draw down
curve
Back water
curve

14. Example 1
Arectangularchannelwithabottomwidthof4.0manda
bottomslopeof0.0008hasadischargeof1.50m
3
/sec.In
agraduallyvariedflowinthischannel,thedepthata
certainlocationisfoundtobe0.30m.Assumingn=0.016,
DeterminethetypeofGVFprofile.

15. Features of Water Surface Profiles
M
M3 (yo>yc>y)
M2 (yo>y>yc)
M1 (y>yo>yc)
CDL
NDL
Yc
Y
o
E
S=Y+V
2
/2ghorizontal asymptote

16. •M1 –Curve
–Occurs when obstructions to flow, such as weirs, dams, control structures
and natural features, or bends, produce Backwater curves.
–Sub critical flow with y > y
0> y
cand Fr < 1 (1 –Fr
2
) > 0
–Mild slope channel with S
e< S
0S
0-S
e> 0
–water surface for the limit values (∞, y
0) are;
a). Y→, V →0, Fr →0, (1-Fr
2
)= 1 and Y→, V →0, Se →0 , (S
o–S
e)=S
o
The water surface meets a very large depth as a horizontal asymptote.
b). Y→Yo, V →Vo, Se →So , (S
o–S
e)=0
The water surface approach the normal depth asymptotically
Water depth will increase
in the flow direction

17. •M2 –Curve
–Occurs at sudden drop of the channel, at constriction type of transitions and
at the canal outlet into pools
–Water surface will be in Region 2
–Sub critical flow with y
0>y > y
cand Fr < 1 (1 –Fr
2
) > 0
–Mild slope channel with S
e> S
0S
0-S
e< 0
–water surface for the limit values (Y
0, Y
c) are;
a). Y→Yo, V →Vo, Se →So , (S
o–S
e)=0
The water surface approach the normal depth asymptotically
b). Y→Yc, Fr →1, (1-Fr
2
)= 0
The water surface meets the critical depth line Vertically .
Water depth will decrease
in the flow direction






2
1Fr
SS
dx
dy
eo

18. •M3 –Curve
–Occurs when supercritical streams enters a mild slope channel .
–The flow is leading from a spillway or a sluice gate to a mild slope forms
–supercritical flow with y
0> y
c > y and Fr > 1 (1 –Fr
2
) < 0
–Mild slope channel with S
e> S
0S
0-S
e< 0
–water surface for the limit values (Y
0, Y
c) are;
a). Y→Yc, Fr =1, (1-Fr
2
)= 0
The water surface meets the critical depth line Vertically .
b). Y→0 , V →, Se →So , (S
o–S
e)=
The water surface approach the bed with some angel, it may be taken as
Water depth will increase
in the flow direction






2
1Fr
SS
dx
dy
eo 3








c
o
o
y
y
S

19. Features of Water Surface Profiles
S
S3 (yc>yo>y)
S2
(yc>y>yo)
S1 (y>yc>yo)
NDL
CDLY
C
Y
o
E
S=Y+V
2
/2g
horizontal asymptote

20. •S1 –Curve
–produced when flow from steep channel is terminated by deep pool that
created by obstruction like weirs, or dams,
–At the beginning of the curve the flow changes from supercritical to subcritical
flow through a hydraulic
–Supercritical flow with y > y
c> y
0and Fr > 1 (1 –Fr
2
) < 0
–Step slope channel with S
e> S
0S
0-S
e< 0
–water surface for the limit values (∞, y
0) are;
a). Y→, V →0, Fr →0, (1-Fr
2
)= 1 and Y→, V →0, Se →0 , (S
o–S
e)=S
o
The water surface meets a very large depth as a horizontal asymptote.
b). Y→Yc, Fr →1, (1 –Fr
2
)=0
The water surface meets the critical depth line Vertically
Water depth will increase
in the flow direction






2
1Fr
SS
dx
dy
eo

21. •S2 –Curve
–Occurs at entrance region of Steep Channel leading from a reservoir and a
brake grade
–Water surface will be in Region 2
–Sub critical flow with y
c>y > y
oand Fr > 1 (1 –Fr
2
) < 0
–Steep slope channel with S
e> S
0S
0-S
e> 0
–water surface for the limit values (Y
0, Y
c) are;
a). Y→Yc, Fr →1, (1-Fr
2
)= 0
The water surface meets the critical depth line Vertically .
a). Y→Yo, V →Vo, Se →So , (S
o–S
e)=0
The water surface approach the normal depth asymptotically
Water depth will decrease
in the flow direction






2
1Fr
SS
dx
dy
eo

22. •S3 –Curve
–Occurs when free flowfroma sluice gate
–supercritical flow with y
c> y
o> y and Fr > 1 (1 –Fr
2
) < 0
–Steep slope channel with S
e> S
0S
0-S
e< 0
–water surface for the limit values (Y
0, Y
c) are;
Y→0 , V →, Se →So , (S
o–S
e)=
The water surface approach the bed with some angel, it may be taken as
Water depth will increase
in the flow direction






2
1Fr
SS
dx
dy
eo 3








c
o
o
y
y
S

23. C –Curves
H –Curves

24. EXAMPLE 2
•Arectangularchannel6mwideconveys100
m3/secofwater.Thechannelslopeis0.003
forthefirstreachandthenasuddenchange
intheslopeto0.01inthesecondreach.The
manningnforthechannelis0.015.Sketchthe
water-surfaceprofileinthechannel.

25. Assignment 3
•Sketch the flow profile if the slopes in the first
and second reaches of the channel in the
example are interchanged.

26. Features of Water Surface Profiles
Control Sections
•A control section is defined as a section in which a fixed
relationshipexists between the discharge and depthof flow
–Weirs,spillways,sluicegatesaresometypicalexamplesof
structureswhichgiverisetocontrolsections.
–Thecriticaldepthisalsoacontrolpoint.However,itiseffectiveina
flowprofilewhichchangesfromsubcriticaltosupercriticalflow.
–Inthereversecaseoftransitionfromsupercriticalflowtosubcritical
flow,ahydraulicjumpisusuallyformedbypassingthecriticaldepth
asacontrolpoint.

27. Analysis of Flow Profile
•Todeterminetheresultingwatersurfaceprofileinagivencase,oneshouldbe
inapositiontoanalyzetheeffectsofvariouschannelsectionsandcontrols
connectedinseries.
–Abreakingradefromamildchanneltoamilderchannel
•Itisnecessarytofirstdrawthecritical-depthline(CDL)andthenormal-depthline(NDL)forboth
slopes.
•SinceycdoesnotdependupontheslopeforatakenQ=discharge,theCDLisataconstantheight
abovethechannelbedinbothslopes.
•Thenormaldepthy
01forthemildslopeislowerthanthatofthemilderslope(y
02).
–SerialCombinationofChannelSections
•Drawthelongitudinalsectionofthesystem.
•CalculatethecriticaldepthandnormaldepthsofvariousreachesanddrawtheCDLandNDLinall
reaches.
•Markallthecontrols,boththeimposedaswellasnaturalcontrols.
•Identifythepossibleprofiles.