Post on 23-Feb-2018
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Type S - profile
The S1, profile is produced when the flow from a steepchannel is terminated by a deep pool created by anobstruction (weir or dam). At the beginning the flowchanges from (super critical) flow to sub-critical flow throa hydraulic jump.)
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S type profile occurs at the
entrance region of a steep channel
leading from a reser!oir and a
bra"e of grade from mild slope to
steep slope.
S# type profile occurs when the
steeper slope changes to relati!ely
a flatter slope ($ild, %ori&ontal)
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S2and S3Profile
S#
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'ritical, %ori&ontaland Ad!erseslopeType ' profiles yn yc &one-
is absent. '1 and '# profiles
are !ery rare and highly
unstable
Type % profile
There is no region 1 for
hori&ontal channel as yn *The % and %# profiles are
similar to $ and $# profiles.
%owe!er % cur!e has a
hori&ontal asymptote.
Type A - profile
There is no region 1 for
Ad!erse channel as yn *Ad!erse slopes are rather rare
and A and A# cur!ed are
similar to % and %# cur!es.
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+ac" aterand raw own 'ur!es The generaldifferential euation for gradually !aried flow is gi!en by,
+ac"water 'ur!e /or a bac"water cur!e, is
positi!e.For this condition, the above equationindicates two possible cases from GVF Eq.!
"i#
"ii#
)(EqDN
FSS
dxdy
r
fo1
1 2
=
=
-
-
here, 0epresent the slope of the water surface (Sw) with respect to
bottom of the channel Sand Sf represent bed slope and friction slope
of the channel respecti!ely 23 is "inetic energy correction co efficient2/r3 is /roude number of flow which is gi!en by,
d4
dy
gD
VFr=
d4
dy
andFandSS rf 010 2
0 >
010 2
0 rf FandSS
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$ For a %iven dischar%e "
i.e. /riction or +ed Slopeis 5n!erselyproportional to depth
$ For uniform flow! Sf Sw Swhen y yn
$ 5t is clear from $anning3s (or) 'he&y3s formula for a gi!en 678
Sf ' S(if ) * )n
Sf* S( if ) ' )n
+y using these ineualities, we can determine sign of numeratorof abo!e euation. Similarly /r 9 1 (super critical) or /r : 1(sub-critical) we can determine the sign of denominator.
342
22
;
h
f0A
7nS =
Sfmeans
Smeans 2 3
Scmeans
)(EqF
SS
dx
dy
r
fo1
1 2
=
-
-
y
1
y
1
ny
1
cy
1
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+hese two conditions are combined to%ether represents three
surface profiles , Sand S3t)pes.
Analysis of 'ase (i)
$ Profile !
$ Profile S!
Analysis of 'ase (ii)
$ Profile S3!
andFandSS rf 010 2
0 >
cn
yyy >>
nc yyy >>
cn yyy
010 2
0 rf FandSS
Sfmeans 21;y3Smeans 21;yn3
Scmeans 21;yc3
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(i) As y yn= Sf S = dy;d4
pro!ided /r not eual to 213 (flow is not critical) in ?.(1)
in other words surface profile approaches
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0AB
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$ For a %iven dischar%e "
i.e. /riction or +ed Slopeis 5n!erselyproportional to depth
$ For uniform flow! Sf Sw Swhen y yn
$ 5t is clear from $anning3s (or) 'he&y3s formula for a gi!en 678
Sf ' S(if ) * )n
Sf* S( if ) ' )n
+y using these ineualities, we can determine sign of numeratorof abo!e euation. Similarly /r : 1 (sub-critical) or /r 9 1(super critical) we can determine the sign of denominator.
342
22
;
h
f0A
7nS =
Sfmeans
Smeans 2 3
Scmeans
)(EqF
SS
dx
dy
r
fo1
1 2
=
-
-
y
1
y
1
ny
1
cy
1
/ -!e
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+hese two conditions are combined to%ether represents
three surface profiles 2, S2t)pes.
Analysis of 'ase (i)
$ Profile 2!
Analysis of 'ase (ii)
$ Profile S2!
010 2
0 rf FandSS
rawdown 'ur!e /or a drawdown cur!e,d)-d is
negati!e.For this condition, the above equation
indicates two possible cases from GVF Eq.! "i#
"ii#
Sfmeans 21;y3
Smeans 21;yn3
Scmeans 21;yc3
010 2
0 rf FandSS
010 2
0 >rf FandSS
010 2
0 >rf FandSS
nc yyy >
cn yyy >
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e can describe how surface profile
approach the
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Surface water Drofiles
+rea"in Erade or Slope$ Simple situations of a series combination of two channelsections with differing bed slopes are considered.
$ To anslyse a general problem of any channel sectionsand controls, the following steps are to be adopted
0 raw the longitudinal section of the systems.
0 'alculate the critical depth and normal depth to draw '@ F
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ater surface Drofiles based on +rea" in Erade (slope)
steep
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ater surface Drofiles based on +rea" in Erade (slope)
(
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'ontrolSection in Bpen 'hannel /low
$ efinition A 'ontrol section is defined as a section in which a fi4edrelationship e4istsbetween the discharge (7)and depth (y) of flow.
$ eirs, spillways, sluice gates are some typical e4amples of structureswhich gi!e rise to control sections.
$ The flow profile through abo!e e4amples form water profiles whichchanges from sub-critical to supercritical flow. 5n the re!erse case oftransition from supercritical flow to sub-critical flow
$ The critical depth is also control point.
$ Any E/ profile will ha!e at least one control section.
$ A hydraulic jump is usually formed bypassing the critical depth as acontrol point.
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Typical 'ontrol section
$easurable ischarge points in a 0i!er;'anal7f(y)
sub-critical (/r :1) flows ha!e controls in the downstream end while
supercritical (/r91) flows ha!e control sections at the upstream end ofthe channel section
Sub-'riticalflow
Super 'ritical flow
Super 'ritical flow
Sub-'ritical flow