CE2253-APPLIED HYDRAULIC ENGINEERING OPEN CHANNEL FLOW

Transcription

1 CE5-APPLIED HYDRAULIC ENGINEERING (FOR IV SEMESTER) UNIT - I OPEN CHANNEL FLOW M.SUGANYA., B.E., LECTURER DEPARTMENT OF CIVIL ENGINEERING FATIMA MICHAEL ENGINEERING COLLEGE MADURAI

2 UNIT I OPEN CHANNEL FLOW OPEN CHANNEL FLOW - TYPES AND REGIMES OF FLOW - VELOCITY DISTRIBUTION IN OPEN CHANNEL WIDE OPEN CHANNEL SPECIFIC ENERGY CRITICAL FLOW AND ITS COMPUTATION. S.NO MARKS PAGE NO. Define open channel 5. What are the classifications of flow in an open channel? 5. Define steay flow an unsteay flow 5 4. Define Uniform flow an Non-Uniform flow What is rapily varie flow? 6 6. What is graually varie flow? 6 7. What is laminar an turbulent flow? 7 8. What is TRANSITION state? 7 9. Give a brief note on Sub-critical, Critical, Super critical flow Give the formula relating to velocity an ischarge in chezy s formula 7. Give the BAZIN, GANGUILLET-KUTTER, MANNINGS formulas for chezy s constant. 8. Give the formula for total energy. 8. Define specific energy How o you calculate specific energy? 8 5. What is specific energy curve? 9 6. Define critical epth What is critical velocity? 9 8. Represent minimum specific energy in terms of critical epth What is critical flow? 0 0. Define streaming flow. What it is otherwise calle as? 0. When oes a super critical flow occur? 0. What is alternate epth? 0. Comparison between open channel flow an pipe flow 0 4. What are the types of channels? 5. What are regimes of flow? 6. What is wie open channel? 7. What o you mean by velocity istribution in an open channel?

3 8. What are the applications of specific energy? 9. What are the factors affecting Manning s roughness coefficient? 0. What is top with, wette area, wette perimeter, Hyraulic mean raius, hyraulic epth? S.NO 6 MARKS PAGE NO Fin the iameter of a circular sewer pipe which is lai at a slope of in 8000 an carries a ischarge of 800 litres/secon.when flowing half full. Take the value of Manning s N0.0 i) Fin the specific energy of flowing water through a rectangular channel of with 5m when the ischarge is 0 m /s an epth of water is m. (ii) Fin the critical epth an critical velocity of water 4 flowing through a rectangular channel of with 5m, when ischarge is 5m /s. The ischarge of water through a rectangular channel of with 8m,is 5 m /s when epth of flow of water is. m.calculate:specific energy of flowing water, Critical 4 epth an critical velocity, Value of minimum specific energy. 4 i) The specific energy for a 5m wie rectangular channel is to be 4Nm/N.If the rate of flow of water through the channel is 0 m /s.determine the alternate epth of flow. 5 ii) Derive the froue number. 5 Conition for maximum ischarge for given value of specific energy. 6 6 i) Fin the velocity of flow an rate of flow of water through a rectangular channel of 6m wie an m eep, when it is running full. The channel is having be slope as in 000. Take chezy s constant C ii) Fin the slope of the be of a rectangular channel 5m when epth of water is m an rate of flow is given as 0 m³/s. Take chezy s constant, C A flow of water of 00 lts/sec flows own in rectangular flume of with 600mm an having ajustable bottom slope. If chezy s constant C is 56, fin the bottom slope 9 necessary for uniform flow with a epth of flow of 00mm. Also fin the conveyance K of the flume. 8 Fin the ischarge through a trapezoial channel of with 8m an sie slope of horizontal to vertical. The epth 0

4 4 9 of flow of water is.4m an value of Chezy s constant, C 50. The slope of the be of the channel is given in Fin the be slope of trapezoial channel of be with 6m, epth of water m an sie slope of horizontal to 4 vertical, when the ischarge through the channel is 0 m³/s. Take Chezy s Constant, C i) Fin the ischarge of water through the channel shown in the fig. Take the value of Chezy s constant 60 an slope of the be as in 000. ii) Fin the rate of flow of water through a V- Shape channel as shown in the fig. Take the value of C 55 an slope of the be in 000 With neat sketches give the computation of critical flow. i) Derive the equation for minimum specific energy in terms of critical epth ii) How o you obtain the specific energy curve explain 4 briefly? Derive the equation for critical epth. 6 4 i) Give the application of specific energy an ischarge curve. ii) Discharge curve: iii) Uniform flow occurs at a epth of.5 m in a long rectangular channel m wie an lai at a slope of If Manning s N 0.05.Calculate () max height of jump on the flow to prouce the critical epth. () The with of the contraction which will prouce critical epth without increasing the upstream epth of flow 7 4

5 5 APPLIED HYDRAULIC ENGINEERING UNIT I OPEN CHANNEL FLOW OPEN CHANNEL FLOW - TYPES AND REGIMES OF FLOW - VELOCITY DISTRIBUTION IN OPEN CHANNEL WIDE OPEN CHANNEL SPECIFIC ENERGY CRITICAL FLOW AND ITS COMPUTATION. Two Marks Questions an Answers. Define open channel. A liqui flowing at atmospheric pressure through a passage is known as flow in open channels. The flow of water through pipes at atmospheric pressure or when the level of water in the pipe is below the top of the pipe, is also classifie as open channel flow.. What are the classifications of flow in an open channel?. Steay an unsteay flow. Uniform flow an non-uniform flow. Laminar flow an turbulent flow 4. Sub-critical, critical, an super critical flow. Define steay flow an unsteay flow. Steay Flow If the flow characteristics such as epth of flow, velocity of flow, rate of flow at any point in open channel flow o not change with respect to time, the flow is sai to be steay flow. v Q y 0, 0 or 0 t t t Unsteay Flow 5

6 6 If at any point in open channel flow, the velocity of flow, epth of flow or rate of flow at any point in open channel flow changes with respect to time, the flow is sai to be steay flow. v Q y 0, or 0 or 0 t t t 4. Define Uniform flow an Non-Uniform flow. Uniform flow If for a given length of the channel, the velocity of flow, epth of flow, slope of the channel an cross-section remain constant, the flow is sai to be uniform. v S 0 y, 0 S for uniform flow Non uniform flow If for a given length of the channel, the velocity of flow, epth of flow, slope of the channel an cross-section o not remain constant, the flow is sai to be non - uniform flow. v S 0 y, 0 S for non-uniform flow 5. What is rapily varie flow? It is efine as that flow in which epth of flow changes abruptly over a small length of the channel. 6. What is graually varie flow? If the epth of flow in a channel changes graually over a long length of the channel, the flow is sai to be graually varie flow. 7. What is laminar an turbulent flow? 6

7 7 Laminar flow The flow in open channel is sai to be laminar if the Reynols number (R e ) is than 500 or 600 ρvr Reynols number µ Turbulent flow If the Reynols number is more than 000, the flow is sai to be turbulent in open channel flow. 8. What is TRANSITION state? state. If the R e lies between 500 to 000, the flow is consiere to be in transition 9. Give a brief note on Sub-critical, Critical, Super critical flow. Sub critical flow: than. Critical Flow: The flow in open channel is sai to be sub-critical if the Froue number is less F e V gd The flow in open channel is sai to be critical if the Froue number is. Super critical flow: The flow in open channel is sai to be super critical if the Froue number is greater than 0. Give the formula relating to velocity an ischarge in chezy s formula. Velocity V C mi Discharge Q A C mi 7

8 8. Give the BAZIN, GANGUILLET-KUTTER, MANNINGS formulas for chezy s constant. a) Bazin formula C 57.6 K.8+ m b) ganguillet-kutter formula C i N N + ( + ) i m c) Manning s formula 6 C m N. Give the formula for total energy. TOTAL ENERGY z + h + V g 8

9 9. Define specific energy. It is efine as energy per unit weight of the liqui with respect to the bottom of the channel. 4. How o you calculate specific energy? E h + V g h epth of liqui V Mean velocity of flow g Acceleration ue to gravity. 5. What is specific energy curve? It is efine as the curve which shows variation of specific energy with epth of flow 6. Define critical epth. It is efine as the epth of flow of water at which the specific energy is minimum. The epth of flow of water at C is known as critical epth. h c q 7. What is critical velocity? g The velocity of flow at critical epth is known as critical velocity. V c gh Where, V c Critical velocity h c Critical epth g acceleration ue to gravity c 8. Represent minimum specific energy in terms of critical epth. 9

10 0 h E c min Where, h c critical epth E min minimum specific energy 9. What is critical flow? It is efine as that flow at which the specific energy is minimum or the flow corresponing to critical epth is efine as critical flow. V c gh c (or) V c gh c 0 0. Define streaming flow. What it is otherwise calle as? When the epth of flow in a channel is greater than the critical epth (h c ), the flow is sai to be sub-critical flow (or) streaming flow (or) tranquil flow.[f e <.0].. When oes a super critical flow occur? When the epth of flow in a channel is less than the critical epth (h c ),the flow is sai to be super-critical flow(or) shooting flow(or) the torrential flow.(f e >.0). What is alternate epth? In the specific energy curve, the point C correspons to the minimum specific energy an the epth of flow at C is calle critical epth. The epths corresponing to points G & H are calle alternate epth.. Comparison between open channel flow an pipe flow S.No Aspects Open channel flow Pipe flow Causes of flow Gravity flow Hyraulic pressures Geometric of sections May have any shape Generally roun in cross sections Surface roughness Varies wiely with epth of flow Depening upon the material of the 0

11 4 Piezometric hea Z + Y HGL Coincies with the water surface 5 Velocity istribution Maximum velocity occurs at a little istance below the water surface. 6 Law Obeys frous law inertia force /gravity force. pipe Z + P/W HGL oes not coincie with water surface. Maximum at center of pipe an at pipe wall V 0 Obeys Reynols law inertia force/viscous force. 4. What are the types of channels? The types are: i) Natural surface: It has irregular sections of varying shapes. Ex. Rivers, streams etc. ii) A channel without any cover at top is known as open channel.ex. Irrigation channels iii) Prismatic channel: A channel with constant bes slope an the same cross section along its length. iv) Experimental: The cross section of the channel is proportional to any power of epth of flow in channel. Ex;Rectangular,Triangular v) Non Exponential: Trapezoial an circular channel are non exponential channels. 5. What are regimes of flow? Regimes of flow are the result of joint influence of viscosity an gravity. The four common stages of flow, viz, laminar, turbulent, sub critical an super critical flows. TYPES: ) Sub critical laminar ) Super critical laminar ) Sub critical turbulent 4) Super critical turbulent. 6) What is wie open channel? If the with of the channel is equal to or more than ten times the epth of flow it may be calle as wie open channel. For experimental or analytical purposes the flow in

12 general region wie open channel may be consiere as a same as flow in the rectangular channel of infinite with. 7) What o you mean by velocity istribution in an open channel? The non uniform istribution of velocity in an open channel is ue to ) Presence of free surface. ) Frictional resistance along the channel bounary ) The velocity istribution in a channel is measure with help of Pitot tube. 8) What are the applications of specific energy? The application of specific energy is: ) Analysis of flow through channel transmission. ) Flow over raise channel bottom ) Flow through sluice gate openings. 9) What are the factors affecting Manning s roughness coefficient? The factors affecting Manning s roughness coefficient: ) surface roughness ) Channel irregularities ) Silting an scouring 4) Obstruction 5) Size an shape of channel 6) Seasonal changes. 7) Suspene material an be loa. 8) Canal alignment 0) What is top with, wette area, wette perimeter, Hyraulic mean raius, hyraulic epth? Top with is the with of the channel section at the free surface. (The with of the liqui surface exposure to atmospheric pressure).wette area is the cross sectional area

13 of flow section in the channel. Wette perimeter the cross sectional area of flow section of the channel. Hyraulic mean raius (R): R A/P Hyraulic epth (D): D A/T 6 Marks Questions an Answers. Fin the iameter of a circular sewer pipe which is lai at a slope of in 8000 an carries a ischarge of 800 litres/secon.when flowing half full. Take the value of Manning s N0.0 Given: Slope of pipe, I /8000 Discharge Q 800 lts/s 0.8 m /s Manning s, N0.0 Dia of sewer pipe D Depth of Flow, D/ π Area of flow A D X 4 πd 8 πd Wette perimeter πd Hyraulic mean epth, m A/P 8 D/4 πd

14 4 πd Q AC mi 8 X 6 m / N πd 0.8 x /0.0 m /6 x m / x 8 πd 0.8 x /0.0 m + x x D x (D/4) / 0.95 / 4 D 8/ D (9.848) /8.96m X i mi π D x /0.0 x m / x D 8/ ) i) Fin the specific energy of flowing water through a rectangular channel of with 5m when the ischarge is 0 m /s an epth of water is m. With b5m Q 0 m /s h m V Q/area0/b x h 0 /5 x / E h + V /g /.06 x9.8 E + ( ) m (ii) Fin the critical epth an critical velocity of water flowing through a rectangular channel of with 5m, when ischarge is 5m /s. b 5m Q 5 m /s Discharge per unit, q Q/b5/5 m /s 4

15 5 Critical epth h c (q / g) / ( /9.8) / 0.97 m Critical velocity Vc gxh 9.8x c.088 m/s ) The ischarge of water through a rectangular channel of with 8m,is 5 m /s when epth of flow of water is. m.calculate: ) Specific energy of the flowing water ) Critical epth an critical velocity ) Value of minimum specific energy Given: Q 5 m /s b 8m h. m Discharge per unit with Q/b5/8 Velocity of flow, VQ/area5/bx h5/8 x..565 m/s V (.565) (i) Specific energy E h m g 8x9.8 (ii) Critical epth h c q g m (iii) Critical velocity Vc gxh 9.8x m/s. c (iv) Minimum Specific energy (E min ): E min h c x m 4) i) The specific energy for a 5m wie rectangular channel is to be 4Nm/N.If the rate of flow of water through the channel is 0 m /s.determine the alternate epth of flow. b 5m V E 4Nm/N 4m E h + g V Discharge/area Q/b x h 0 /5 x h 5

16 6 Q 0 m /s E 4 V E h + g h+ (4/h) x /g 8 h + gxh 8 4 h + 9.8xh h + h 4h h (or) h 4 h This is a cubic equation solving by trial (or) error h.9 m an 0.48 ii)derive the froue number. The square root of ratio of inertia force of flowing liqui to gravity force F e Fi F g F i ρ AV mass * acceleration F g M g ρ ADg D wette area / Top with of channel A/T F e ρav ρadg V Dg V Dg 5) Conition for maximum ischarge for given value of specific energy. The specific energy at any section of channel is given 6

17 7 E y + V g ; V Q A Q by E y + Q b y g E y Q b y g Q (E-Y) b y g b g [Ey y ] Q b y g( Ey.. () For ischarge Q to be maximum to expression Ey y shoul be maximum Hence ifferentiate () with respect to y an equate it to zero Q y b [ [ ] g Ey y *[ g[ Ey y ] b g( Ey y * g(ey y ) ) Q y 0 bg(ey y g( Ey y ) ) 0 E bgy bgy 0 E / y y / E Maximum Discharge: 7

18 8 Q b g( y y ) Q b Q b gy g( E * E E Q max.705 b E / The specific energy is minimum when it is equal to / times value of epth of critical flow. Here the equation () represents the specific energy an is equal to / times the epth of flow. Therefore the equation () represents the specific energy an y is the critical epth. Hence the conition for maximum ischarge for given value of specific energy is that the epth of flow shoul be critical. 6) i) Fin the velocity of flow an rate of flow of water through a rectangular channel of 6m wie an m eep, when it is running full. The channel is having be slope as in 000. Take chezy s constant C 55. Given: With of rectangle channel, b 6m. Depth m Solution: Area b 6 8m² Be Slope, i in 000 /000 Chezy s constant C 55 Perimeter P b+ 6 + m Hyraulic mean epth, m A/P 8/.5m V C.5 / m/s Q V Area m³/s. ii) Fin the slope of the be of a rectangular channel 5m when epth of water is m an rate of flow is given as 0 m³/s. Take chezy s constant, C 50. Given: With of channel b 5m. Depth of water m Rate of flow Q 0 m³/s. C 50 Be Slope i Solution: Q AC mi 8

19 9 A Area b 5 0 m² m A/P 0/ (b+) 0 / (5+ ) 0 /(5+4) 0/9 m /9 i 0/9 i 0/500 /50 0i/9 4/500 i 4/500 9/0 6/5000 /5000/6 / Therefore Be slope is in ) A flow of water of 00 lts/sec flows own in rectangular flume of with 600mm an having ajustable bottom slope. If chezy s constant C is 56, fin the bottom slope necessary for uniform flow with a epth of flow of 00mm. Also fin the conveyance K of the flume. Given: Discharge Q 00 lts/s 00/ m³/s. b 600mm 0.6m 00mm 0.m A b m² C 56 Slope of be i Solution: Hyraulic mean epth, m A/P 0.8/(b+) 0.8/( ) 0.8/. 0.5m Q AC mi i 0.5 i 0./(0.8 56) Squaring on both sies 0.5i (0.0/0.8 56) ² i / // /54 Therefore Slope of the be is in 54. Conveyance K of the channel Q AC mi Q K i Where, K AC m Conveyance of channel section K AC m m³/s. 8) Fin the ischarge through a trapezoial channel of with 8m an sie slope of horizontal to vertical. The epth of flow of water is.4m an value of Chezy s constant, C 50. The slope of the be of the channel is given in Given: With b 8m Sie Slope horizontal to vertical Depth.4m Chezy s constant C 50, Be Slope I /4000 9

20 0 Depth CF.4 Solution: Horizontal ts BE.4 / 0.8m Therefore Top With of the channel, CD AB + BE m Therefore Area of trapezoial channel, ABCD is given as, A (AB + CD) CE/ (8+9.6).4/ 7.6..m² Wette Perimeter, P AB + BC + AD AB BC BC BE² + CE² (0.8)² + (.4)².59m P m Hyraulic mean epth m A/P./ m Q AC mi /4000. m³/s. 9) Fin the be slope of trapezoial channel of be with 6m, epth of water m an sie slope of horizontal to 4 vertical, when the ischarge through the channel is 0 m³/s. Take Chezy s Constant, C 70 Given: Be With, b 6.0m Depth of flow,.0m Sie Slope Horizontal to 4 vertical Discharge Q 0 m³/s Depth of flow CE m Chezy s Constant 70 CE m BE ¾ 9/4.5m Therefore Top With, CD AB + BE m Wette Primeter, P AD + AB + BC AB + ABC ( BC AD) AB + (BE² + CE²) (.5) ² + () ².5m A Area of trapezoial ABCD (AB+CD) CE / (6+0.50)/ 4.75m² Hyraulic mean epth, m A/P 4.75/.50.8 Q AC mi i 45.6 i i (0/45.6) ² /(45.6/0) ² /6 i /6 0) i) Fin the ischarge of water through the channel shown in the fig. Take the value of Chezy s constant 60 an slope of the be as in 000. Given: Chezy s Constant C 60 Be Slope, i /000 0

21 Solution: A Area ABCD + Area BEC (..0) + лr²/.6 + (.5) ² л/ 7.4m² Wette Perimeter, P AB + BEC + CD. + лr л m Hyraulic mean epth, m A/P 7.4/ Q AC mi (.00 /000) m³/s ii) Fin the rate of flow of water through a V- Shape channel as shown in the fig. Take the value of C 55 an slope of the be in 000 Given: C 55 Be Slope i /000 Depth of flow, 4.0m Angle mae by each sie with vertical i.e <ABD <CBD 0º Solution: Area A Area of ABC * Area of ABCD (*AD* BD)/ AD * BD BD tan 0º *BD 4tan 0º*4 9.76m² Wette Perimeter, P AB + BC AB (BD² + AD²) (4) ² + (4tan0º)² ( ) 9.75m Therefore Hyraulic mean epth, m A/P 9.76/9.75.0m Q AC mi 9.76 * 55* (*/000) 6.066m³/s Empirical Formula for the value of Chezy s constant: Derive the imension of C: V C mi Chezy s formula C V/ mi L/T/ (A/P)i L/T/ (L²/Li) L/T Li L* L/T Li L/T L½ T ¹ [ i is imensionless] C L½ T ¹ Tan0 AD/BD AD BDtan0 (AB BC) ) With neat sketches give the computation of critical flow. Critical flow an its computations:

22 Critical state of flow in an open channel has the following properties:. The specific energy is a minimum for a given ischarge.. The ischarge is a maximum for a given specific energy.. The specific force is minimum for a given ischarge 4. The velocity hea is equal tom half the hyraulic epth. 5. The foun number is unity. 6. The slope of the channel that sustains a ischarge of a uniform epth equal to critical epth is calle critical slope. 7. A control section is one where a efinitive stage (epth) ischarge. 8. A critical flow section is excellent control section because, at that section. Q Q c A square of gd by x square root of gy, if the cross section is rectangular. Typical cross sections: ) i) Derive the equation for minimum specific energy in terms of critical epth. Minimum special energy in terms of critical epth. Specific energy is given by q E h + gh () The specific energy is minimum when epth of flow is critical an hence the above eqn. q E min h c + gh c () q But h c g ()

23 hc Using () in () we get E min h c + hc E min h c ii) How o you obtain the specific energy curve explain briefly? Specific energy curve may be obtaine by rawing a curve for specific energy E against epth of flow Y. Diagram: Consier a rectangular section in which a steay but non uniform flow is talking place. B with of channel Y epth of flow Q ischarge through channel Velocity of flow V A Q Q bh q h q ischarge per unit with. Specific energy E h + q h g

24 4 q h + gh E E p + E k The specific energy plat entails the following information: ) The curve for potential energy is E p h is a straight line passing through the origin making an angle 45 0 with each of the two axis (X & Y) ) The curve for kinetic energy (E k ) is a parabola. ) Plot for specific energy is obtaine by aing kinetic energy to potential energy. 4) Specific energy is asymptotic to the horizontal axis for small values of y an asymptotic to 45 0 lines for high values of y. 5) At a certain epth h c calle critical epth the specific energy curve as a point of minimum specific energy, the corresponing flow velocity is calle critical velocity V c. 6) If a line is rawn through the point C,the area above that line is known as the area of sub critical flow (F e < ).Area below that line is known as super critical flow (F e < ) 7) For energy value of specific energy other than minimum there are two possible epth of flow (h & h ).One greater than critical epth. & other less than critical epth. This two epth for the same specific energy are referre to as alternate or conjugate epth. ) Derive the equation for critical epth. Critical epth (Y c ) The epth of flow at which the specific energy is minimum is calle critical epth. (y c ). The epth is sai to be critical at any section of F e is equal to one. F e v gd The mathematical expression for critical epth can be obtaine by ifferentiating the specific energy equation with respects to an equates it to zero. 4

25 5 q E h + gh e h q + hg () q - gh h q g 0 But specific energy is min, the epth of flow is critical, Therefore, From eq (); h c q g q - 0 gh q gh q We know that V h Sub V h q in eq () () v () gh V v gh gh F e the epth is known as critical epth. 4) i) Give the application of specific energy an ischarge curve. 5

26 6 Applications of specific energy: Analysis of flow through channel transmission Flow over raise channel bottom Flow through sluice gate openings. ii) Discharge curve: For a constant specific energy the ischarge per unit with (q) is plotte against epth of flow, the curve is known as ischarge curve; In this fig. q attains max value at a particular value of h. iii) Uniform flow occurs at a epth of.5 m in a long rectangular channel m wie an lai at a slope of If Manning s N 0.05.Calculate () max height of jump on the flow to prouce the critical epth. () The with of the contraction which will prouce critical epth without increasing the upstream epth of flow. Given: Soln: y.5 m i b m N 0.05 Y c R q g b b +.5X + x C R N 6 (0.75) 0.05 C 64 V C mi x V.66 m/s Q A x V.5 xx m /s q Q/b 7.48 /.49 6

27 7 y c q g y c 0.859m z Max y V yc g.66 x0.859 x z Max 0.504m y + v Yc + g Vc g Yc Yc + x Yc/.64 q g.09 q / q q Q/b b.5795 b

28 CE5- APPLIED HYDRAULIC ENGINEERING (FOR IV SEMESTER) UNIT II- UNIFORM FLOW Compile by, M.SUGANYA., B.E., LECTURER DEPARTMENT OF CIVIL ENGINEERING FATIMA MICHAEL ENGINEERING COLLEGE MADURAI COMPILED BY VERIFIED BY HOD AI PRINCIPAL

29 S.NO 6 MARKS PAGE NO... a) A rectangular channel of with, 4m is having a be slope of in 500. Fin the maximum ischarge through the channel. Take value of C 50 b) A rectangular channel carries water at the rate of 400 lt is when be slope is imension of the channel of C 50. in 000. Fin the most economical A rectangular channel 4m has epth of water.5 m. The slope of the be of the channel is in 000 an value of chezy s constant C 55. It is esire to increase the ischarge to a maximum by changing the imensions of the section for constant area of cross-section, slope of the be an roughness of the channel. Fin the new imension of the channel an increase in ischarge A trapezoial channel has sie slopes to. It is require to ischarge.75 m /s of water with a be graient of in 000. If unline the value of chezy s C is 44. If line with concrete, its value in 60. The cost per m of excavation is four times the cost per m of lining. The channel is to be the most efficient one fin whether the line canal or the unline canal will be cheaper. What will be the imension of hat economical canal? A power canal of trapezoial section has to be excavate through har clay at the least cost. Determine the imensions of the channel given, ischarge equal to 4 m /s be slope :500 an Manning s N 0.0 A trapezoial channel with sie slope of to is to be esigne to convey 0m /s at a velocity of m/s. So that the amount of concrete line for be sie is minimum Calculate the area of lining require for m length of channel. What are the factors to be consiere for non eroible channels give some examples an explain how to etermine 6 8 9

30 the coefficient? Briefly explain the measurement of flow of irregular channel? A trapezoial channel has sie slopes of horizontal to vertical an the slope of the be is in 500. The area of the section is 40 m. Fin the imensions of the section if it is more economical. Determine the ischarge of the most economical X n if C 50 A trapezoial channel has sie slopes of horizontal to 4 vertical an slope of its be is in 000. Determine the optimum imensions of the channel, if it is to carry water at 0.5 m /s. Take chezy s constant 80. A trapezoial channel with sie slopes of to has to be esigne to convey 0 m /s at a velocity of m/s so that the amount of concrete lining for the be an sies is the minimum. Calculate the area of lining require for one meter length of canal

31 4 UNIT- II UNIFORM FLOW Uniform flow Velocity measurement Manning s & Chezy s formula etermination of roughness coefficients Determination of normal epth an velocity Most economical sections Non-eroible channels. Two Marks Questions an Answers. Define uniform flow. For a given length of channel the velocity of flow, epth of flow, slope of channel the c/s remain constant the flow is sai to be uniform flow. V S 0, y S 0,. Define channel of most economical sections. A channel which given maximum which given maximum ischarge for a given cross sectional area an le slope is calle a channel of most economical gross-section. It can also be efine as the channel that has a minimum wette perimeter, so that there is a minimum resistance to flow an thus resulting in a maximum ischarge.. What are the conitions to be most economical section? The conitions to be most economical for the following shapes of the channels will be consiere.. Rectangular channel. Trapezoial channel. Circular channel 4. Relate ischarge with wette perimeter. Q AC mi A AC i P K, Where K AC A i Cons tan t P m A p 4

32 5 Q will be maximum when the wette perimeter P is minimum 5. Give the conitions for a rectangular channel to be most economical. A rectangular channel to be most economical is:. b. m Where, b with of the channel epth of the channel m hyraulic mean epth. 6. What is the conition for the most economical trapezoial section?. b + n n + Half of top with one of the sloping sie. m. A semi circle rawn form O with raious equal to epth of flow will touch the three sies of the channel. 7. Give the formula to fin the with an perimeter for a trapezoial section to be most economical. i.) b ii.) P. P b For a slope of 60 o, the length of sloping sie is equal to the with of the trapezoial section. 8. Give the two conitions for the circular channel to be most economical. 5

33 6. Conition for maximum velocity. Conition for maximum ischarge. 9. Give the conition for maximum velocity an maximum ischarge.. Conition for maximum velocity for circular section. 0.8 D D iameter of the circular channel. m 0. D m hyraulic mean epth.. Conition for maximum ischarge for circular section 0.95 D 0. What are the factors affecting chezy s an manning s N formula?. Surface roughness an vegetation.. Irregularity in crosssection.. Obstruction to flow 4. Sitting 5. Depth flow an ischarge 6. Size & shafe of the channel 7. suspene an be particles 8. Personal changes which after the flui viscosity.. Give the chezy s formula. V c mi Q A C mi Where, Q ischarge m hyraulic mean epth A area C Chezy s constant 6

34 7. Drive the imension of C V c mi C V mi L / T A i P L / T L i L T L Li L L T Li L T L T / (I imension) C L T /. Give the Bazin formula. C 57.6 K 8+ m m hyraulic mean epth (or) hyraulic raius K Bazin s constant (epens upon the roughness of the surface of the channel) 4. Represent Kutter s formula in MKS Units C i N N + + i m N i M Roughness Co-efficient (or) Kutter s constant Slope of the be hyraulic mean epth 5.Give the manning s formula C m / 6 N m N hyraulic mean epth Manning s constant (same value as Kutter s Constant) 7

35 8 6. What are non- eroible channel? Most line channel an built up channel scan withstan erosion satisfactorily an they are consiere non eroible. In esigning non eroible channel, the factors such as max permissible velocity, maximum tractive force are not to be consiere. 7. What are the factors to be consiere are?. The kin of material forming channel boy. To etermine the roughness co-efficient.. The maximum permissible velocity to avoi the eposition of silt 8. Give some non-eroible materials. The materials are: Concrete Stone masonry Steel Cast iron Timber Glass Plastic 9. How o you fin mean velocity of flow? The mean velocity of flow is foun by,. Pitot tube. Floats. Current meter. 0. What is current meter? A current meter is an instrument use to measure the velocity of flow at a require point in the flowing stream. It consists of wheel or revolving element containing blaes or cups an tail on which flat vane or fins are fixe.. On what the value of chezy s constant C epens? Its value epens upon the roughness of the insie surface of the channels. If the surface is smooth there will be less frictional resistance to the motion of water. Therefore C will have more value an it leas to velocity, ischarge increase. If the surface is rough- vice versa.. Define channels of most economical sections? A channel which gives maximum ischarge for a given cross-sectional area an be slope is calle a channel of most economical cross-section. It is channel which involves least excavation for a esigne amount of ischarge. A Channel that has a maximum wette perimeter, so that there is a minimum resistance to flow an thus resulting in a maximum ischarge. 8

36 9 6 MARKS QUESTIONS AND ANSWERS ) a) A rectangular channel of with, 4m is having a be slope of in 500. Fin the maximum ischarge through the channel. Take value of C 50 Given: b 4 m i C b (or) b 4. 0m m. 0m Area of economical rectangular channel, A b 4 8m ( ) Q AC m i m /s. 500 (b) A rectangular channel carries water at the rate of 400 lt is when be slope is in 000. Fin the most economical imension of the channel of C 50 Given: Q 400 lts/s 0.4 m /s, i, C For the rectangular channel to be most economical, i. With b. ii. Hyraulic mean epth m Area b Q AC mi / / b m / ( 0.5) 0. m 5 / 9

37 0. A rectangular channel 4m has epth of water.5 m. The slope of the be of the channel is in 000 an value of chezy s constant C 55. It is esire to increase the ischarge to a maximum by changing the imensions of the section for constant area of cross-section, slope of the be an roughness of the channel. Fin the new imension of the channel an increase in ischarge. Given, b 4m. A b x 4 x m.5 m i, C Wette perimeter, P + b + D m A 4 m P Q AC mi m / s 000 For max ischarge for a given area, slope of be an roughness. Let b new with of channel new epth of flow Area A b x, where A 6 m B b x Max ischarge b b New imension b. 464m. 7 m Wette perimeter p + b Hyraulic mean epth, A 6 m m P

38 .7 m n Max ischarge Q AC m i m / s. 000 Increase in ischarge Q Q m / s. A trapezoial channel has sie slopes to. It is require to ischarge.75 m /s of water with a be qraient of in 000. If unline the value of chezy s C is 44. If line with concrete, its value in 60. The cost per m of excavation is four times the cost per m of lining. The channel is to be the most efficient one fin whether the line canal or the unline canal will be cheaper. What will be the imension of hat economical canal? Given, Sie slope n Slope of be i 000 Q.75 m /s For unline C 44 Line C 60 Cost per m of excavation 4 x cost per m of lining. Let the cost per m of lining x Cost per m of excavation 4x. For most efficient trapezoial channel, Hyraulic mean epth i m b epth of channel with of channel. Half of top with length of sloping sie b + n n + b + + b

39 b 0.88 ( b + n ) ( ) A A.88. For unline channel: C 44 Q A V A C mi Q AC mi Q A.88, m / / m. Subs in () we get, b m Cost of excavation per running meter Length of unline channel / ( 7.645).56m. Volume of channel x Cost per m of excavation. (Area of channel x ) x4 x [( b + n ) ] 4x ( ).56 4x 7. 5x.For line channels Value of C 60 Q A C m i

40 Subs the value of A from equn () an m ( Q Q.75) / 5 / m subs in () b x m The cost of lining In the case of line channel Cost of excavation Cost of excavation Volume of channel x cost per m of excavation. l A [( b + n ) ] x 4x ( ).99 4x 9. 0x Cost of lining Area of lining x cost per m of lining P x (Perimeter of lining x ) x x b n + + x ( ) x ( ) x 7. 8x

41 4 Total cost 9.0 x + 7.8x 6.9 x The total cost of line channel 6.9 x Unline channel 7.5 x. Hence Line channel will be cheaper. Dimensions b.649 m.99m 4. A power canal of trapezoial section has to be excavate through har clay at the least cost. Determine the imensions of the channel given, ischarge equal to 4 m /s be slope :500 an Manning s N 0.0 Given: Q 4 m /s N 0.0 i 500 The trapezoial section shoul be most economical for the excavation of the canal at the least cost. Sie slope (Value of n) is not given. Hence the best sie slope for most economical trapezoial section is given by equation. n For most economical section, Half of top with Length of one of sloping sie b + n n + For n 4

42 5 b + + b n Area of trapezoial section, A ( b + n ) + A Hyraulic mean epth for most economical section, m Q AC mi where C m / 6 N 6 Q m / m N 500 / 6 m +.7 m / /.7 8 / 8 / / 8 / / (.844) (.844). m b. 008m.7 5

43 6 5. A trapezoial channel with sie slope of to is to be esigne to convey 0m /s at a velocity of m/s. So that the amount of concrete line for be sie is minimum Calculate the area of lining require for m length of channel. n Q 0m /s. V m/s Q A V Q 0 A 5m V n b + n + n b + y b + g (.88) b A ( b + n ) 5 ( ) m, b.69m. Area for m length A m Wette perimeter x length ( b + ) + n [ ] + A m 6.6 m 6

44 7 6. What are the factors to be consiere for non eroible channels give some examples an explain how to etermine the coefficient? Most line channels an buil up channels can with stan erosion satisfactorily an they are consier non eroible. In esigning non-eroible channel the factors such as max permissible velocity, max tractive force are not be consiere. The esigner simply compute the imension of channel by a uniform flow an the ecies the final imension on the basics of hyraulic efficiency or empirical rule of best section practically an economically. The factors to be consiere are, The kin of material forming channel boy To etermine the roughness co-efficient The minimum permissible velocity to avoi the eposition of silt an epers. Channel bottom an sie slope free boar etc all forms the most efficient section. Some on-eroible: Concrete Stone masonry Steel Cast iron timber Class Plastic The selection of the material epens mainly on the availability of Cost of the material. Metho of construction. Purpose for which the channel to be use. Determination of Manning Roughness Co-efficient: For the etermination of roughness co-efficient N is so ifficult for that there is no exact metho of selecting n value. The experience engineer can calculate by means soun engineering jugment an experience. For beginners it can be no more than guess an ifferent iniviual will \obtain ifferent results. 7

45 8 Approaches for Determination of N;. To unerstan factor that effect the value of N an narrow the problem by guess work.. To construct a table typical N values for channels of various types.. To examine an become familiar with appearance of some typical channel whose roughness co-efficient are known. 4. To etermine value of N by analytical proceure base on the theoretical velocity istribution in the channel C/s an on the ata of either velocity or roughness co-efficient. 7. Briefly explain the measurement of flow of irregular channel? The term irregular channel inclues large river an small streams. In case of small streams flow can be obtaine by filling notch or weir across the stream an it is not possible in case of large rivers. Increase of large rivers, ischarge is equal to Area of flow x mean velocity of flow Simple segment metho. Simpson s rule. Simple segment metho: In this metho, the C/s of river is ivie into number of segments AB, BC, CD etc as shown in fig. 8

46 9 C/s of river with unequal segments. l, l, l,.. An,,, Length of the segment AB, BC, CD mean epth of respective segments. Area of flow area of segment AB Area of segment BC + l b + l b + l b Simpson s Rule: In this metho the whole river with in ivie into even number of equal segments, so that there are o number of epths take an en of each segment as shown in fig. l A 0 lost ( + ) + ( + + ) + ( + ) l length of each segment. 6, epth taken at the en of segment. Mean Velocity of flow Pitot tube Single float Floats Double float Ro float. Current meter. 9

47 0 Pitot Tube: A pitot tube is a simple evice use for measuring the velocity of flow at the require pt in the flowing stream. It consists of a glass tube bent at right angles The tube is ippe vertically I the flowing stream with its lower open en facing irection of flow, upper open en projecting above the water level in the stream. The water rises up in the tube ue to pressure exerte y the flowing water. By measuring rise of water in table. The velocity of water V calculate by, V gh h g heat of water in the tube aove the water surface acceleration ue gravity. Floats: A float is a small object mae of woo or other suitable material which is lighter than the water an thus capable of floating on surface. The surface velocity at any section may be obtaine by single float. The time taken by the float to traverse a known istance is measure. Surface velocity (V S ) Distance travele by float Time taken to travel the istance 0

48 Mean velocity of flow 0.8 to 0.95 V S Double Float: A ouble float consists of a surface float on which it is attache with a hollow metal sphere heavier than water an suspene from it by a chor of known length.. The epth of lower float may be regulate by the length of chor.. The velocity is obtaine by noting the time taken y the float to traverse a known istance.. Double float irectly gives the value of mean velocity. Ro Float: It consists of vertical wooen ro which is weighte at bottom to keep it vertical.

49 The length of ro is so ajuste that it reaches bottom of the stream. The ro will travel with a velocity equal to the mean velocity of the section. Current Meter: A current meter is an instrument use to measure the velocity of flow at a require pt in the flowing stream. It consists of wheel or revolving element containing blaes or cups an tail on which flat vans or fins are fixe. CUP TYPE: The current meter accoring to revolving element may be classifie into. Cup type. Screw type. Propeller type Series of conical cup mounte on a spinle, the spinle hel vertical at right angle to irection of flow SCREW TYPE: The revolving element consists of shaft with its axis parallel to the irection of flow which carries a number of curve vanes mounte on periphery of shaft. In orer to measure the velocity of flow water submerge uner water an motion of water in the stream activate it riving the wheel at a spee proportional to the velocity of flow. An electric current is passe from the battery to the wheel by means of wire. The rotation of wheel makes an breaks the electric circuit which causes an electric bell to ring. Thus by counting the ringing bell the rotation of wheel an hence the velocity of flowing water is calculate. 8. A trapezoial channel has sie slopes of horizontal to vertical an the slope of the be is in 500. The area of the section is 40 m. Fin the imensions of the section if it is more economical. Determine the ischarge of the most economical X n if C 50 Sie slope, n Horizontal Vertical Be slope, i, C

50 Area of section, A 40 m For the most economical section, b + n n + b + (or) + b b.8. 6 Area of trapezoial section, ( b + n ) b + A ( b + n ) A m.76 b m Discharge for most economical X n 4.80 m. 40m Q AC m i Q 80m / s 9. A trapezoial channel has sie slopes of horizontal to 4 vertical an slope of its be is in 000. Determine the optimum imensions of the channel, if it is to carry water at 0.5 m /s. Take chezy s constant 80. Given, Horizontal n, i Vertical Q 0.5 m /s. C 80

51 4 The conition for most economical section, b + n n + b b b.5. 5 b For the ischarge, Q z AC mi, m (most eco X n ) 0.5 A Area of trapezoial X n, ( b + n ) A / m.5 b 0.55 m Optimum imensions of the channel are with epth 0.55m. 4

52 5 0. A trapezoial channel with sie slopes of to has to be esigne to convey 0 m /s at a velocity of m/s so that the amount of concrete lining for the be an sies is the minimum. Calculate the area of lining require for one meter length of canal. Given: Horizontal n Vertical Sie slope Q 0 m /s. V m/s Discharg e 0 Area 5m Velocity For most economical trapezoial section, Half of the top with one of the sloping sie. b + n n + For n, the conition becomes b + n n + n b + n +.44 ( b + n) ( ) A.88 A 5 m b 0.88 n m.88 b m Area of lining require for one meter length of canal Wette perimeter x length of canal P x l P b + n m Area of lining x m 5

53 CE5- APPLIED HYDRAULIC ENGINEERING (FOR IV SEMESTER) UNIT III VARIED FLOW Compile by, M.SUGANYA., B.E., LECTURER DEPARTMENT OF CIVIL ENGINEERING FATIMA MICHAEL ENGINEERING COLLEGE MADURAI COMPILED BY VERIFIED BY HOD AI PRINCIPAL

54 CONTENTS S.NO MARKS PAGE NO. What is graually varie flow? 5. What are the assumptions mae which eriving an equation for G.V.F? 5. Fin the rate of change of epth of water in a rectangular channel of 0m wie an m eep when the water is flowing with a velocity of m/s. The flow of water through 5 the channel of be slope in 4000, is regulate in such a way that energy line is having a slope of Sketch back water curve an affux? 6 5. Define Affux 6 6. What is back water curve an length of back water curve? 7. What are the basic equations of GVF? 6 8. What are the classifications of channel flow? 7 9. What are the classifications of GVF profiles? 8 In a rectangular channel m wie, epth.6 m with a velocity of m/s. The be slope of channel is in If the flow of water through the channel is regulate 8 in such away the energy line having a slope of Fin the rate of change of epth of water in the channel.. What is the Critical slope? 9. What is Mil slope? 9. What is Steep slope? 9 4. Define Horizontal slope Define averse slope How o you classify the water curves? 0 7. What are the points to be remembere while stuying the flow profiles? 8. What are the three zones of channel be? 0 9. What are the three methos to calculate Surface profiles in 6 0

55 prismatic channel? 0. Give the formulas relate to Direct Step Metho S.NO 6 MARKS PAGE NO.. Derive the equation of graually varie flow (or) Nonuniform flow slope of free water surface? Fin the slope of the free water surface in a rectangular channel of with 0m having epth of flow 5m. The. ischarge through the channel is 50 m /s. The be of the channel is having a slope of in Take the value of Chezy s constant C 60. Give the expression of the length of Back water curve? Determine the length of the back water curve cause by an 4. affux of.0 m in a rectangular channel of with 40m an epth h.5m. The slope of the be is given as in 000. Take Manning s N With a neat sketch give the graually varie flow profiles (or) briefly escribe water curves or flow profiles 9 6. Briefly explain Graphical Integration Metho

56 4 UNIT III VARIED FLOW Dynamic equations of graually varie flow-assumptions- Characteristics of flow profiles - Draw own an back water curves Profile etermination Graphical integration, irect step an stanar step metho flow through transitions.. What is graually varie flow? Two marks Questions an Answers If the epth of flow in a channel changes graually over a long length of the channel the flow is sai to be graually varie flow an is enote by G.V.F.. What are the assumptions mae which eriving an equation for G.V.F?. The be slop of the channel is small. The flow is steay an hence ischarge Q is constant. Accelerative effect is negligible an hence hyrostatic pressure istribution prevails over channel cross-section. 4. The energy correction factor, α is unity, α 5. The roughness Co-efficient is constant for the length of the channel an it oes not epen on the epth of flow. 6. The formula such as Chezy s formula, Manning s formula, which are applicable, t the uniform flow are also applicable to the GVF graually varie flow for etermining the slope of energy line. 7. The channel is prismatic. Fin the rate of change of epth of water in a rectangular channel of 0m wie an m eep when the water is flowing with a velocity of m/s. The flow of water through the channel of be slope in 4000, is regulate in such a way that energy line is having a slope of Given, 4000 b 0 m V m/s Be slope, i h m Slope of energy line,, i let the rate of change of epth of water b e h x 4

57 5 ( i i ) h b e x V gh Sketch back water curve an affux? Consier the flow over a am. On the upstream sie of the am, the ept of water will be rising. It there ha not been any obstruction (such as am ) in the path of flow of water in the channel, the epth of water woul have been constant as shown by otte lien parallel to the be of the channel. Due to abstraction, the water level rises an it has maximum epth from the be at some section. 5. Define Affux. Affux is efine as the maximum increase in water level ue to abstraction in the path of flow of water. Affux ( h ) h h h epth of water at the point, where water starts rising up. maximum height of rising water from be. 6. What is back water curve an length of back water curve? The profile of the rising water on the upstream sie of the am is calle back water curve. The istance along the be of the channel between the section. Where water starts rising to the section where water is having maximum height is known as length of back water curve. 7. What are the basic equations of GVF? /. / V R S S f f 4 / 4 / n n V R n A Q R 5

58 6 Water surface slope Be slope S ω water surface S O - be The basic ifferential equation governing the graually varie follow is y x S o S Q ga T f Written in terms of (e) Specific energy E x S o S f y y 0 y C actual epth normal epth Critical epth 8. What are the classifications of channel flow? CATEGORIES OF CHANNEL S.No Channel Characteristic Symbol category conition Remarks Mil slope M h A >hc critical Sub critical flow at normal epth. Steep slope S H c >h A Super critical flow at normal epth Critical slope C h c h A Critical flow at normal epth 4 Horizontal be H S 0 0 Cannot sustain uniform Y 0 flow 5 Averse slope A S 0 <0 Cannot sustain uniform flow 6

59 7 9. What are the classifications of GVF profiles? Classification of GVF profiles Channel Conition Type Mil slope h > h n > h C h > h > n h C h > hc > n h C h > h c > h n M M M S Steep slope Critical slope Horizontal be Averse slope h > h > C h n hc > hn > h h > ( h c h n ) ( ) h c h n h > h c > h h > h < h > h < h c h c h c h c S S C C H H A A 0. In a rectangular channel m wie, epth.6 m with a velocity of m/s. The be slope of channel is in If the flow of water through the channel is regulate in such away the energy line having a slope of Fin the rate of change of epth of water in the channel. Given, b m, h.6m V. m/s, b, 4000 i i e 7

60 8 h x ib ie V gh (or) ib ie.89 0 F e 4. What is the Critical slope? The channel bottom is sai as critical when the bottom slopes (So) is equal to the critical slope Sc. S o Sc In this case, normal epth of flow will be equal to the critical epth h n h c. What is Mil slope? The channel bottom is sai as mil when the bottom slope S o is less than critical slope S c. In this case the normal epth of flow is greater than critical epth S O < S c h n > h c. What is Steep slope? Channel bottom is sai as steep when the bottom slope (S o ) is greater than critical slope Sc. S > o S c In this case, the normal epth of flow will be less than the critical epth ( h n < h c ) 4. Define Horizontal slope. The channel bottom is sai as horizontal when the bottom slope (S o ) is zero. 8