CE 6403 APPLIED HYDRAULIC ENGINEERING UNIT - III RAPIDLY VARIED FLOW

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1 CE 6 APPLIED HYDRAULIC ENGINEERING UNIT - III RAPIDLY VARIED FLOW Application of the energy equation for RVF - Critical epth an velocity - Critical, Sub-critical an Super-critical flow - Application of the oentu equation for RVF - Hyraulic jups -Types - Energy issipation - Surges an surge through channel transitions BY MRKUMARG ME STRUCTURAL ENGINEERING ASSISTANT PROFESSOR DEPARTMENT OF CIVIL ENGINEERING SRI VENKATESWARA COLLEGE OF ENGINEERING SRIPERUMBUDUR 6 7

2 Hyraulic Jup A hyraulic jup occurs when flow changes fro a supercritical flow (unstable) to a sub-critical flow (stable) There is a suen rise in water level at the point where the hyraulic jup occurs Rollers (eies) of turbulent water for at this point These rollers cause issipation of energy A hyraulic jup occurs in practice at the toe of a a or below a sluice gate where the velocity is very high

3 Location of hyraulic jup Generally, a hyraulic jup occurs when the flow changes fro supercritical to subcritical flow The ost typical cases for the location of hyraulic jup are: Jup below a sluice gate Jup at the toe of a spillway Jup at a glacis (glacis is the nae given to sloping floors provie in hyraulic structures)

4 General Expression for Hyraulic Jup In the analysis of hyraulic jups, the following assuptions are ae: () The length of hyraulic jup is sall Consequently, the loss of hea ue to friction is negligible () The flow is unifor an pressure istribution is ue to hyrostatic before an after the jup () The slope of the be of the channel is very sall, so that the coponent of the weight of the flui in the irection of the flow is neglecte Expression for Depth of Hyraulic Jup V g Depth of Hyraulic Jup ( - )

5 Expression for Loss of Energy Due to Hyraulic Jup [ Expression for Depth of Hyraulic Jup in Ters of Upstrea Froue Nuber ] [ ] 8 ( F ) e Length of Hyraulic Jup This is efine as the length between the two sections where one section is taken before the hyraulic jup an the secon section is taken ieiately after the jup For a rectangular channel fro experients, it has been foun equal to 5 to 7 ties the height of the hyraulic jup

6 The epth of flow of water, at a certain section of a rectangular channel of wie, is The ischarge through the channel is 5 ³ / sec eterine whether a hyraulic jup will occur, an if so, fin its height an loss of energy per kg of water Given ata Wie of channel (b) Depth of flow ( ) Discharge ( Q ) 5 ³ / sec Solution q Q / b 5 / 75 ² / sec Critical Depth ( y c ) y c ( 57 ) Critical Depth ( y c ) y c y c q g 9 8 Now the epth on the upstrea sie is This epth is less than critical epth an hence hyraulic jup will occur < y c

7 g V where q v ) ( g q 8 9 ) 75 ( Height of Hyraulic Jup ( - ) ( 86 ) ( ) ( )

8 Loss of Energy [ ] h L [ 86 ] 86 Answer *Loss of Energy kg / kg / kg kg The epth of flow of water, at a certain section of a rectangular channel of wie, is 5 This ischarge through the channel is 6 ³ / sec If a hyraulic jup takes place on the ownstrea sie, fin the epth of flow after the jup Given ata Wie of channel (b) Depth of flow ( ) 5 Discharge ( Q ) 6 ³ / sec Fin out epth of flow after the jup ( )?

9 g V Solution q Q / b 6 / ² / sec Where q v ) ( g q ) ( 5 5 Answer * epth of flow after the jup ( ) 6 ( ) ( )

10 A hyraulic jup fors at the ownstrea en of spillway carrying 79 ³ / sec ischarge If the epth before jup is 8, eterine the epth after the jup an energy loss Given ata Depth before jup ( ) 8 Discharge ( Q ) 79 ³ / sec Fin out epth after the jup ( )? Fin out energy loss ( )? Solution Taking with b, we get q Q / b 79 / 79 ² / sec Where q v g V ) ( g q ) 9 (7 8 8

11 ( ) ( 9 6 ) 8 66 Loss of Energy [ ] h L [ ] 8 66 Answer *Depth of flow after the jup ( ) 866 *Loss of Energy 7 5

12 A sluice gate ischarges water into a horizontal rectangular channel with a velocity of / sec an epth of flow of Deterine the epth of flow after the jup an consequent loss in total hea Given ata Depth of flow before hyraulic jup ( ) Velocity of flow before hyraulic jup ( V ) / sec Fin out epth after the jup ( )? Fin out loss in total hea ( )? Solution q V x / ² / sec V Where q v g V ) ( g q 8 9 ) ( ( )

13 ( 5 5 ) Loss in Total Hea [ ] h L [ - ] 7 Answer * epth of flow after the jup ( ) * Loss in Total Hea 7

14 5 A sluice gate ischarges water into a horizontal rectangular channel with a velocity of 6 / sec an epth of flow is The with of the channel is 8 Deterine whether a hyraulic jup will occur, an if so, fin its height an loss of energy per kg of water Also eterine the power lost in the hyraulic jup Given ata Velocity of flow ( V ) 6 / sec Depth of flow ( ) With of channel ( b ) 8 Fin out epth of hyraulic jup ( )? Fin out Height of Hyraulic Jup ( - )? Fin out loss of energy ( )? Fin out Power Lost? Solution q Q / b ( V x Area ) / b ( V x x b ) / b ( V x ) (6 x ) ² / sec Froue Nuber on the upstrea sie, [ ] F e V g

15 [ ] F e 6 98 [ ] 9 F e As Froue Nuber is ore than one, the flow is shooting on the upstrea sie Shooting flow is unstable flow an it will convert itself into streaing flow by raising its height an hence hyraulic jup will take place ( i ) Depth of hyraulic jup ( ) [ ] 8 ( F ) e [ ] 8 ( 9 ) 55 [ 7 65 ]

16 ( ii ) Height of Hyraulic Jup ( - ) ( 55 ) 5 ( iii ) Loss of Energy per kg of water [ ] [55 ] kg / kgofwater ( iv) Power Lost in kw g ρ Q Where Q A x V ( x b ) x V Q ( x 8 ) x 6 9 ³ / sec P h L P P kw

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