type s - profile for water surface profiles

7/24/2019 Type S - Profile for water surface profiles

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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.)


2/18

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#


4/18

'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


7/18

+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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9/18

(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


10/18

0AB


11/18

$ 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


12/18

+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 >


13/18

e can describe how surface profile

approach the


14/18

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


15/18

ater surface Drofiles based on +rea" in Erade (slope)

steep


16/18

ater surface Drofiles based on +rea" in Erade (slope)

(


17/18

'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.


18/18

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

type s - profile for water surface profiles

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