UNIT 1 OPEN CHANNEL FLOW 2 MARK QUESTIONS AND ANSWERS

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1 DEPARTMENT: CIVIL ENGINEERING SEMESTER: IV- SEMESTER SUBJECT CODE / Name: CE53 / Applied Hydrauli Engineering 1. Define open hannel flow with examples. Examples: UNIT 1 OPEN CHANNEL FLOW MARK QUESTIONS AND ANSWERS Flow of liquid with a free surfae (i.e., surfae exposed to atmosphere) through any passage is known as open hannel flow. The liquid flowing through any losed passage without touhing the top an also treated as open hannels. 1. Flow in natural waterfalls, river and streams. Flow in artifiial or man-made hannels suh as irrigation hannels and flumes. 3. Closed onduit or pipe arries liquid partially (sewers that arry domesti or industrial waste water). Generally, liquid flowing in open hannel in water.. Explain laminar and turbulent flow. (a) Laminar flow: If Reynolds number of flow is less than 500, it is alled as Laminar flow. The value of Reynolds number is between 500 and 000, the flow is transitional. (b) Turbulent flow: For values of Reynolds number greater than 000, the flow is turbulent. 3. What are the various types of flow in open hannels? The flow in open hannel is lassified into the following types: (a) Steady and unsteady flow (b) Uniform and non- uniform flow () Laminar and turbulent flow (d) Subritial, ritial and superritial flow. 4. Define the term uniform flow. If the depth of flow, slope of the bed of hannel and ross setion remain onstant with respet to distane is alled uniform flow. y V 0, 0 s s IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 1

2 5. Define non uniform flow. Flow properties, suh as depth of flow, veloity of flow are not onstant with respet to distane is alled non uniform flow. y V 0, 0 s s 6. Distinguish between steady and unsteady flow. In steady flow, various harateristis of flowing fluids suh as veloity, pressure, density, temperature et. at a point do not hange with time. In other words, a steady flow may be defined as that in whih the various harateristis are independent of time. Mathematially it an be expressed as u v w 0, 0 ; 0 t t t p 0, 0 t t In unsteady flow, various harateristis of flowing fluids suh as veloity, pressure, density, et. at a point hange with respet to time. Mathematially, v p 0 and ( or) 0... t t et Unsteadiness refers to the hange of flow pattern with the passage of time at a position in the flow. 7. Explain the terms: (i) Gradually varied flow and (ii) Rapidly varied flow. [Anna Univ.Nov 07&Nov 08] 1. Gradually varied flow If the depth of flow hanges gradually over a long length of the hannel, the flow is said to gradually varied flow (GVF) IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page

3 . Rapidly varied flow. If the depth of flow hanges rapidly over a small length of the hannel, the flow is said to be rapidly varied flow. 8. Write down the formula for Froude number Froute Number F V gd 1.0 Where V = Average veloity of flow in m/s g = Aeleration due to gravity =9.81 m / s D = Hydrauli depth in meter Cross Setion Area of flow Top Width 9. Define hydrauli mean depth. A T D = Hydrauli depth in meter Cross Setion Area of flow Top Width A T 10.Define speifi energy. [Anna Univ.Nov 06&Nov 08] Speifi energy of a flowing liquid is defined as energy per unit weight of a liquid with respet to the bottom of the hannel. By a symbol E. Where V E y g E = Speifi Energy V = Veloity of flow y = Depth of flow IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 3

4 11. Define ritial flow. Depth of flow of water at whih the speifi energy. E is minimum is alled as ritial depth (y) For retangular hannel, ritial depth, 1.Define ritial veloity. h q g 1 3 Veloity of flow at the ritial depth is alled ritial veloity V V g* y Where y = Critial Depth g = Aeleration due to gravity 13.Distinguish between ritial, sub ritial and subritial flows. Critial flow: Depth of flow of water at whih the speifi energy is minimum is alled as ritial flow. Otherwise, flow orresponding to ritial depth is alled as ritial flow. For Critial Depth Froute Number F V gd 1.0 Where D Hydrauli Mean Depth Area of flow Top Width A T Sub ritial flow: When the depth of flow in a hannel is greater than the ritial depth y, the flow is alled as sub ritial flow. It is otherwise, alled as streaming flow or tranquil flow. For sub ritial flow, Froude number, F<1 IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 4

5 Sub ritial flow: When the depth of flow in a hannel is less than the ritial flow, y, the flow is alled as sub ritial flow or torrential flow. For superritial flow, Froude number, F>1 14. Differentiate prismati and non-prismati hannels. Prismati hannel Geometri dimensions of the hannel, suh as ross setion and bottom slope are onstant throughout the length of the hannel is alled as a prismati hannel. Eg. Most of the artifiial hannels of irular, retangular, trapezoidal and triangular ross setion are alled prismati hannels. Non- prismati hannel Geometri dimensions of the hannel, suh as ross setion and bottom slope are onstant for length of the hannel is alled as a non-prismati hannel. Eg. All natural hannels suh as river, are non-prismati hannels. 15. Explain speifi fore (F) [Anna Univ. Nov 08] Speifi fore is the sum of the pressure fore (F) and momentum fore due to flow (M) per unit weight of the liquid at a setion. Speifi Fore F Where s F M weight density of Liquid 16.What is speifi energy and what is ondition for obtaining only one depth for a given speifi energy? [Anna Univ. May 07] Total Energy on open hannel flow V E Z y g Considering the hannel bed as datum line, z 0 IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 5

6 Speifi Energy E V y g From Speifi Energy urve, Corresponding to the Minimum speifi energy E, there is only one depth of floe that is alled Critial depth (min) 17. Differentiate losed flow losed onduit flow and open hannel flow. [Anna Univ. May 07] S.No Closed onduit flow Open hannel flow 1. Water does not have with free surfae. Water flows with a free surfae.. Water does not ontat with atmosphere pressure but it has only hydrauli Water ontents with atmospheri pressure. pressure. 3. Flow may be due to either by pump pressure or by gravity flow Flow is obtained only by gravity. 18.Define sub ritial flow: If the Froude number is less than one then the flow is said to be sub ritial flow 19.Define ritial flow: If the Froude number is less equal to one it is alled as ritial flow. 0.Define superritial flow: If the Froude number is greater than one it is alled as super ritial flow 1. What are the possible types of flow in open hannel with respet to spae and time? A. steady and unsteady flow B. uniform and non-uniform flow IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 6

7 .what do you know about uniform and non uniform flow? Uniform flow: If the given length of the hannel,depth,veloity,the rate of flow, ross setion are onstant. Non Uniform flow: If the given length of the hannel,depth,veloity,the rate of flow, ross setion are not onstant. 3.Define speifi energy: It is defined as energy per unit weight of the liquid with respet to the bottom of the hannel. 4.Define ritial depth: It is defined as the depth of flow of water at whih the speifi energy is minimum. 5.Define ritial veloity: The veloity of flow at the ritial depth is known as ritial veloity. 6.Define gradually varying flow If the hange in depth in a varying flow is gradual so that the urvature of the streaming line is not exessive suh flow is alled gradually varying flow. 7.Define Rapidly varying flow If the urvature in a varied flow is large and depth hanges appreiably over short length it is alled rapidly varying flow. 8.What are the onditions of retangular hannel of best setion? The two onditions are breadth is equal to two times the depth (b=d) and hydrauli mean depth is equal to half the depth (m=d/) 9.What do you mean by open hannel flow? 1.Open hannel flow has a free surfae whih is subjeted to atmospheri pressure..in open hannel flow the ross setion is irregular. 30.List the instrument used to measure open hannel flow 1.pitot tube.ultrasoni flow instrument. 3.Dropper instrument 4.Gurley instrument. IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 7

8 31.What are the assumptions of gradually varying flow profile? 1.Pressure distribution at any setion is assumed to be hydrostati..the veloity distribution at the hannel setion is fixed 3.The hannel is prismati 4.The roughness oeffiient is independent of the depth of flow 3.What do you mean by speifi energy urve? It is defined as the urve whih shows the variation of speifi energy with respet to depth of flow. 33.Define open hannel flow? The term open hannel flow denotes the gravity-driven flow of a liquid with a free surfae. 34.What do you mean by stream lining? Streamlining is adding a faired tail setion to redue the extent of separated flow on the downstream portion of an objet. 35. What do you meant by Open hannel flow? Give few Examples. Open Channel Flow is defined as fluid flow with a free surfae open to the atmosphere. Examples inlude streams, rivers and ulverts not flowing full. Open hannel flow assumes that the pressure at the surfae is onstant and the hydrauli grade line is at the surfae of the fluid. 36. Define the term Critial depth Depth of flow at whih speifi energy is a minimum; depth in a onduit at whih maximum flow will our if the onduit is at ritial slope, the water is flowing at ritial veloity, and an adequate supply of water exists. 37. What is meant by Critial Slope The slope at whih maximum flow will our at minimum veloity; the slope equal to loss of head per foot resulting from flow at a depth giving uniform flow at ritial depth. 38. Define the term Hydrauli Gradient Pressure gradient, or a line representing pressure or piezometrihead in a pipe flowing full, or the water surfae in open hannel flow. IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 8

9 39. What is meant by Hydrauli jump A hydrauli jump is a phenomenon in the siene of hydraulis whih is frequently observed in open hannel flow suh as rivers and spillways. When liquid at high veloity disharges into a zone of lower veloity, a rather abrupt rise ours in the liquid surfae. The rapidly flowing liquid is abruptly slowed and inreases in height, onverting some of the flow's initial kineti energy into an inrease in potential energy, with some energy irreversibly lost through turbulene to heat. In an open hannel flow, this manifests as the fast flow rapidly slowing and piling up on top of itself similar to how a shokwave forms IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 9

10 16 MARK QUESTIONS AND ANSWERS 1.Calulate the Speifi energy,critial depth and the veloity of the flow of 10 m 3 in a ement lined retangular hannel.5m wide with m depth of water. Is the given flow is sub ritial or super ritial Given Data SOLUTION: To find Q = 10 m 3 /s b =.5 m y = m 1. Speifi Energy. Critial Depth 3. Veloity for the flow STEP 1: To find the Speifi Energy: V Q 10 E y V m / s g A.5* E *9.81 E 0.0 m E.0 m STEP : To find Critial Depth: y 1 3 q g Q b.5 q 4 m / s 1.18 m IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 10

11 STEP 3: Veloity of flow: V g * y 9.81* m/ s STEP 3: To find weather the flow is Sub ritial of Super ritial: F V g* D 9.81* Hene the flow is Sub-ritial. A Trapezoidal hannel has a bottom width of 6.1 m and side Slopes of H : 1 V.When the depth of the flow is 1.07 m. The flow is m 3 /s. What is the Speifi energy of flow? Is the Flow is sub ritial or super ritial Given Data SOLUTION: b = 6.1 m m = m Q = 1.07 m 3 /s To find 1. Speifi Energy. 3. Flow is tranquil or Rapid STEP 1: To find the Speifi Energy: A b my y 6.1* m IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 11

12 V Q A m/ s V E y g 1.19 E 1.07 * 9.81 E 1.14 m STEP 3: To find weather the flow is Sub ritial of Super ritial: V F g* D A D T A b my y 6.1 * m T b my 6.1 * * m D D 0.85 m Finally we an get F * F Hene the flow is Tranquil flow or Sub-Critial Flow IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 1

13 3. Calulate the Speifi Energy of 1 m 3 /s of water flowing with a veloity of 1.5 m 3 /s in a Retangular hannel 8 m wide. Find the depth of water in the hannel when the Speifi energy would be minimum. What would be the value of Critial as well minimum Speifi Energy Given Data SOLUTION: To find V = 1.5 m / s m = m b = 8 m 1. Speifi Energy. Critial veloity 3. minimum Speifi Energy STEP 1: To find the Speifi Energy: Q Q Q V * A A b* d V V note Q d V * b A b * d 1 b 1 m y 1.5 * 8 We Know that b y, Finally we Will Get V E y g * m Critial Depth (h ) is given by ( y ) IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 13

14 y or h q g 1 3 note Q b 1 8 q 1.5 m / s m 1 3 STEP : To find the Critial veloity V : V g * y 9.81* m/ s STEP 3: To find the minimum Speifi Energy: 3 E min y E min 3 * m 4. A 8 m wide Channel onveys 15 umes of water at a depth of 1. m. Determine the (1) Speifi energy of the flowing water () Critial depth, Critial veloity and minimum Speifi Energy (3) Froude number and the weather flow is sub-ritial or Super-ritial Given Data V = 1.5 m / s m = m b = 8 m IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 14

15 SOLUTION: To find (1) Speifi energy of the flowing water () Critial depth, Critial veloity and minimum Speifi Energy (3) Froude number and the weather flow is sub-ritial or Super-ritial STEP 1: To find the Speifi Energy: V Q A 15 8* m / s V E y g * m Step : To find Critial Depth Q b 15 8 q m / s y q g 1 3 y m IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 15

16 Step 3 :To find Critial Veloity V g * y 9.81* m/ s Step 4 :To Minimum Speifi Energy: 3 E min y E min 3 * m Step 5 :To find the Froude Number: F V gd V gy note D A b* y T b y * Hene the Flow is Sub-Critial IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 16

17 5. Find the ritial depth for a speifi energy of 1.5 m in: (1) Retangular hannel of bottom width m () Triangular hannel of side slope 1:1.5 Given Data E = 1.5 m SOLUTION: To find ritial depth for Retangular Trapezoidal and Triangular Channel Step 1 :Retangular Channel: E 3 y E * 3 y 1.5* 3 y y 1.0 m Step :Triangular Channel: E 5 y 4 E 4 * 5 y 1.5*4 5 y y 1.0 m IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 17

18 6. A Trapezoidal hannel with side slope of H:3V Has to arry 0 m 3 /s. Find the slope of the hannel when the bottom width of the hannel is 4 m and the depth of the water is 3 m.take manning s n=0.03 Given Data SOLUTION: b = 4 m y = 3 m m = m Q = 0 m 3 /s n = 0.03 To find Slope of the trapezoidal Channel A b my y 4 * 3 30 m P b my 4 * * 3 16 m A R P m Use manning s onstant Formulae C 1 N R 1 6 IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 18

19 1 1 (1.875) To find the Slope of the Channel Q AC RS 18* * S Take Square root onboth Sides * 1369 * * S * S S S This is the required Slope range for the given Trapezoidal Channel. IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 19

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22 9. How do you lassify open hannels? Explain in detail. Also explain the veloity distribution in open hannel. (AUC Nov/De 010) IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page

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25 10.Write short notes on the following: (i) Critial flow and its omputations (ii) Channel Transition (AUC Nov/De 010) 1. Critial flow and its omputations i) Critial flow: Depth of flow of water at whih the speifi energy is minimum is alled as ritial flow. Otherwise, flow orresponding to ritial depth is alled as ritial flow. For Critial Depth Froute Number F V gd 1.0 Where D Hydrauli Mean Depth IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 5

26 ii)sub ritial flow: When the depth of flow in a hannel is greater than the ritial depth y, the flow is alled as sub ritial flow. It is otherwise, alled as streaming flow or tranquil flow. For sub ritial flow, Froude number, F<1 iii)sub ritial flow: When the depth of flow in a hannel is less than the ritial flow, y, the flow is alled as sub ritial flow or torrential flow. For superritial flow, Froude number, F>1.Channel Transition: IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 6

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30 11. Define speifi energy. How would you express the speifi energy for a wide retangular hannel with depth of flow D and veloity of flow V? Draw the typial speifi energy diagram and explain its features. It is defined as energy per unit weight of the liquid with respet to the bottom of the hannel. The extra information needed to solve the above problem an be provided by the speifi energy equation. Speifi energy, Es, is defined as the energy of the flow with referene to the hannel bed as the datum: Total Energy on open hannel flow V E Z y g Considering the hannel bed as datum line, z 0 Speifi Energy E V y g From Speifi Energy urve, Corresponding to the Minimum speifi energy E, there is only one depth of floe that is alled Critial depth (min) IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 30

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32 For steady flow this an be written in terms of disharge Q For a retangular hannel of width b, Q/A = q/y This is a ubi in y. It has three solutions but only two will be positive (so disard the other). IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 3

33 1. Define Froude number F R. Desribe the flow for F R =, F R < and F R >1. Represent a disharge versus depth urve for a onstant speifi energy and explain its features. Froude Number Froude number in onnetion with open surfae flow is defined as V/ gl. In the ase of open hannel flow, the harateristi length, l, is the depth y and V is the flow veloity. Hene Froude number an be represented by the ratio, Flow veloity/wave veloity. As already indiated, there are three possible flow situations namely (V/) < 1, (V/) = 1 and (V/) > 1 or the Froude number for the flow is less than or equal to or greater than 1. IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 33

34 Case (i) If Fr < 1, then V < and any disturbane an travel upstream. The downstream onditions an hange the flow onditions upstream. Suh a flow is alled subritial or tranquil flow. Only gradual hanges our in suh a situation. Case (ii) Fr = 1. The flow is alled ritial flow. Disturbanes annot travel upstream. A standing wave may generally result. Case (iii) Fr > 1, suh flows are alled superritial or rapid or shooting flows. Disturbanes annot travel upstream. Downstream onditions annot be felt upstream. Changes our only in the downstream flow. These are similar to subsoni, soni and supersoni flows in the ase of flow of ompressible fluids where Math number is the governing fator also defined as V/, where is the soni speed or veloity of propagation of small disturbane in the fluid. 13.How are the flows lassified under speifi energy onepts? It is defined as energy per unit weight of the liquid with respet to the bottom of the hannel. The extra information needed to solve the above problem an be provided by the speifi energy equation. Speifi energy, Es, is defined as the energy of the flow with referene to the hannel bed as the datum: Total Energy on open hannel flow V E Z y g Considering the hannel bed as datum line, z 0 Speifi Energy E V y g From Speifi Energy urve, Corresponding to the Minimum speifi energy E, there is only one depth of floe that is alled Critial depth (min) IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 34

35 ***ALL THE BEST*** IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 35

36 1.0. QUESTION BANK PART A 1. Differentiate open hannel flow from pipe flow.. What is speifi energy and is the ondition for getting only one depth for a given speifi energy? 3. How will do you distinguish between ritial, sub- ritial, super- ritial flow. 4. Sketh the veloity distribution in a trapezoidal hannel. 5. What is the use of a pitot tube? 6. Briefly write a note on anemometers 7. Find the relationship between Chezy's C and Manning's n. 8. Sketh the veloity distribution in retangular and triangular hannels. 9. What are the possible types of flow in open hannel with respet to spae and time? 10. What are the equations for ritial depth for retangular hannel? 11. Distinguish between steady uniform flow and unsteady non uniform flow. 1. Define speifi energy. IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 36

37 PART B 1. Explain any two formulae for estimation of veloity in open hannels?. A trapezoidal hannel has side slopes of 1 horizontal to vertial and the slope of the bed is 1 in 000. The area of the setion is 4 m. Find the dimensions of the setion if it is to be most eonomial. Determine the disharge of the most eonomial setion of C = Desribe various types of flow in an open hannel. 4. A retangular hannel with a base width of 0.60 m arries a disharge of 100 lps. The Chezy's C is 60. If the depth of flow is 0.5 m, determine the bed slope of the hannel 5. In a flow through a retangular hannel for a ertain disharge froude number orresponding the two alternate depths are y1 and y. show that (F /F 1 ) (3/) =(+F )/(+F1 ) 6. A retangular hannel 1.5m wide and depth.5m, disharge is 10m3/se. alulate the speifi energy and depth alternate to the given depth. 7. A trapezoidal hannel has a bottom width 6m, and side slope of h to 1v if a depth of flow is 1.m at a disharge of 10m3/se. ompute the speifi energy and ritial depth. 8. Define wide open hannel and also what are the important assumptions in hydrauli parameters? 9. The retangular hannel arries a disharge of 30m3/se. The bottom width of the hannel is 6.0m and flow veloity is 1.75m/se. Determine two alternate depths possible in the hannel. 10. If y 1 and y are alternate depths in a retangular hannel show thaty C 3 = (y 1 y ) / (y1 + y ) And hene the speifi energy E = (y 1 + y1 y + y ) / (y1 + y ) 11. For a onstant speifi energy of 3.0m, what maximum flow may our in a retangular hannel of 4.5m bed width? 1. The speifi energy for a 3m wide hannel is 8N.m/N. What is the maximum possible disharge in the hannel? IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 37

38 13. Show that in a retangular hannel maximum disharges ours when the flow is ritial for a given value of speifi energy. 14. The speifi energy for a 5m wide retangular hannel is 4m, the disharge of water through the hannel is 19umes. Determine the alternate depths of flow. 15. Show that the minimum speifi energy in a retangular hannel is 1.5 times the ritial depth. 16. Show that the relation between alternate depths y1 and y in a retangular hannel an be 3 expressed by y 1 y /(y1 +y )=y where y is the ritial depth of flow. 17. For a onstant energy of.4n.m/n. Calulate the maximum disharge that may our in a retangular hannel 4m wide. 18. For a purpose of disharge measurement the width of a retangular hannel is redued gradually from 3m tom and floor is raised by 0.3m at a given setion when the approahing depth of flow is m, what rate flow will be indiated by a drop of 0.15m in the water surfae elevation at the ontrated setion? 19. How to estimate the hydrauli jump and draw sketh of the jump? IV Semester CE53 / Applied Hydrauli Engineering by P.Dhanabal AP / Civil Page 38