CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW CE5- APPLIED HYDRAULIC ENGINEERING (FOR IV SEMESTER) UNIT II- UNIFORM FLOW
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW CE5- APPLIED HYDRAULIC ENGINEERING (FOR IV SEMESTER) UNIT - II
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW DEPARTMENT OF CIVIL ENGINEERING CONTENTS S.NO MARKS PAGE NO. Define uniform flow. 6. Define channel of most economical sections. 6. What are the conitions to be most economical section? 6 4. Relate ischarge with wette perimeter 6 5. Give the conitions for a rectangular channel to be most economical. 7 6. What is the conition for the most economical trapezoial section? 7 7. Give the formula to fin the with an perimeter for a trapezoial section to be most economical 7 8. Give the two conitions for the circular channel to be most economical. 7 9. Give the conition for maximum velocity an maximum ischarge. 8 0. What are the factors affecting chezy s an manning s N formula? 8. Give the chezy s formula. 8. Drive the imension of C 9. Give the Bazin formula. 9 4. Represent Kutter s formula in MKS Units 9 5. Give the manning s formula 9 6. What are non- eroible channel? 0 7. What are the factors to be consiere are? 0 8. Give some non-eroible materials. 0 9. How o you fin mean velocity of flow? 0 0. What is current meter? 0. On what the value of chezy s constant C epens? 0. Define channels of most economical sections? 0
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW 4 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.. 4. 5. 6. 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 the coefficient? 6 8 9 4
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW 5 7. 8. 9. 0. 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. 0 4 5 7 5
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW 6 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 A m p Q will be maximum when the wette perimeter P is minimum 6
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW 7 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.. Conition for maximum velocity. Conition for maximum ischarge. 7
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW 8 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 8
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW 9. 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. 57.6 C 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 0.0055 + + C i N 0.0055 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) 9
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW 0 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. 0
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW 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 50 5000 b (or) b 4. 0m m. 0m Area of economical rectangular channel, A b 4 8m ( ) Q AC m i 4 50 0.8 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 50 000 For the rectangular channel to be most economical, i. With b. ii. Hyraulic mean epth m Area b Q AC mi 000 5 000 5 / 0.4 50 50.58 0.4 5 / 0.5 577.58 b 0.577. 54m / ( 0.5) 0. m 5 /
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW. 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.5 6.0 m.5 m i, C 55 000 Wette perimeter, P + b + D.5 + 4 +.5 7. 0m A 4 m 0.857 P 7 Q AC mi 6.0 55 0.857 9.66m / 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 6 6 b.7.464.7 New imension b. 464m. 7 m Wette perimeter p + b +.7 +.464 +. 7 6.98 Hyraulic mean epth, A 6 m 0. 866m P 6.98
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW.7 m 0. 866n Max ischarge Q AC m i 6 55 0.866 9.7m / s. 000 Increase in ischarge Q Q 9.7 9.66 0.05m / 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. 0. 88
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW 4 b 0.88 ( b + n ) ( 0.88 + ) A A.88. For unline channel: C 44 Q A V A C mi Q AC mi.75.88 44 000 Q A.88, m.88 44 000 5 /.75 000 5 5 / 7.45.88 44.56m. Subs in () we get, b 0.88 0.88.56. 868m 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 (.868 +.56).56 4x 7. 5x.For line channels Value of C 60 Q A C m i 4
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW 5 Subs the value of A from equn () an m.75.88 60 ( Q Q.75) 000.88 60 000 5 / 5 /.75 000.88 60 5.606.99m subs in () b 0.88 0.88 x.99.649 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 (.649 +.99).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 (.649 +.99 + ) x (.649 +.99 ) x 7. 8x 5
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW 6 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 6
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW 7 b + + b n A + + Area of trapezoial section, ( 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 0.0 500 / /.7 8 / 8 / 4.0.7.09 / 8 / 4.0.09.844 / 8 0.75 (.844) (.844). m 605.605 b. 008m.7 7
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW 8 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 0.88. A ( b + n ) 5 ( 0. 88 + ).75.654 m, b.69m. Area for m length A m Wette perimeter x length ( b + ) + n [.69 +.654] + A m 6.6 m 8
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW 9 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. 9
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW 0 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. 0
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW 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 5 4 4+ ( + ) + ( + + ) + ( + ) 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.
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW 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
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW 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.
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW 4 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 5000 4
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW 5 Area of section, A 40 m For the most economical section, b + n n + b + (or) + b + +.8 4 b.8. 6 Area of trapezoial section, ( b + n ) b + A ( b + n) A.6 +.76 40 40.76 4. 80m.76 b.6.6 4.80 5. 9m Discharge for most economical X n 4.80 m. 40m Q AC m i 40 50.4 Q 80m / s 500 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 4 000 Q 0.5 m /s. C 80 5
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW 6 The conition for most economical section, b + n n + b + 4 4 + 5 4 b +.5.5 b.5. 5 b For the ischarge, Q z AC mi, m (most eco X n ) 0.5 A 80 000 Area of trapezoial X n, ( b + n ) A 4 7 4 +.75 0.5.75 80 000.5 5/ 0.5 0. 55m.5 b 0.55 m Optimum imensions of the channel are with epth 0.55m. 6
CE5-APPLIED HYDRAULIC ENGINEERING/UNIT-II/UNIFORM FLOW 7 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) ( 0.88 + ) A.88 A 5 m b 0.88 n 5 5.88.658. 654m.88 b 0.88 0.88.654. 69m Area of lining require for one meter length of canal Wette perimeter x length of canal P x l P b + n +.69 +.654 + 6. 047m Area of lining 6.047 x 6.047 m 7