CE6403 APPLIED HYDRAULIC ENGINEERING UNIT 1 UNIFORM FLOW

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1 CE6403 APPLIED HYDRAULIC ENGINEERING UNIT 1 UNIFORM FLOW Definition and differences between pipe flow and open channel flow - Types of Flow - Properties of open channel - Fundamental equations - Velocity distribution in open channel - Steady uniform flow: Chezy equation, Manning equation - Best hydraulic sections for uniform flow - Computation in Uniform Flow - Specific energy and specific force - Critical depth and velocity. 1. Define pipe flow. A pipe is a closed conduit which carries water under pressure. The flow in a pipe completely fills the cross section and there is no free surface of water termed as pipe flow. 2. Differentiate pipe flow and open channel flow. S.No Pipe flow Open channel flow 1 In pipe flow, the flow takes Open channel flow takes place by gravity force. place by hydraulic pressure. 2 Pipes are generally circular cross section. Open channels may have any shape such as triangular, rectangular, trapezoidal and circular. 3 Hydraulic gradient line(hgl) HGL coincides with the water surface. does not coincide with the water surface. 4 Velocity distribution is symmetrical about the pipe The shape of the velocity profile is dependent on the channel roughness. axis. 5 The maximum velocity occurring at centre of the pipe. Maximum velocity occurs at a little distance below the water surface. 6 Flow cross section is fixed. Flow cross section depends on depth of flow. 3. What are the characteristics of open channel flow? For open-channel flow, the flow surface is open to atmosphere. Open-channel flows are almost always turbulent, unaffected by surface tension.

2 The pressure distribution within the fluid is hydrostatic. Pressure is constant along water surface. 4. Define open channel flow with examples. Flow of liquid in a free surface through any passage is known as open channel flow. The liquid flowing through any closed passage without touching the top can also be treated as open channel flow. Examples: (i) (ii) (iii) Flow in natural waterfalls, rivers and streams. Flow in artificial or man-made channels such as irrigation channels and flumes. Closed conduit or pipe carries liquid partially(sewers that carries domestic and industrial waste water). 5. What are the various types of flow in open channels? The flow in open channel is classified into the following types: (a) Steady and unsteady flow (b) Uniform and non-uniform flow (c) Laminar and turbulent flow (d) Sub-critical, critical and super-critical flow. 6. Define uniform flow and non-uniform flow in channels. Uniform flow: If the depth of flow, slope of bed of channel and cross section remains constant with respect to distance, it is called uniform flow. Non-uniform flow: ( y s ) = 0, ( V s ) = 0 Flow properties, such as the depth of flow, velocity of flow are not constant with respect to distance is called non-uniform flow. ( y s ) 0, ( V s ) 0 7. Define steady and unsteady flow. In steady flow, various characteristics of flowing fluids such as velocity, pressure, density, temperature etc., at a point do not change with time. ( u t ) = 0, ( V t ) = 0 ( p s ) = 0, ( ρ s ) = 0

3 In unsteady flow, various characteristics of flowing fluid such as velocity, pressure, density etc., at a point change with respect to time. ( v t ) 0, ( p t ) 0 8. Explain the terms (i) Gradually varied flow and (ii) Rapidly varied flow. (i) (ii) Gradually varied flow: If the depth of flow changes gradually over a long length of the channel, the flow is said to be gradually varied flow. Rapidly varied flow: If the depth of flow changes rapidly over a small length of the channel, the flow is said to be rapidly varied flow. 9. What are rigid channels? Channels can withstand erosion resulting from high velocities of water called as rigid or non-erodible sections. Channels which are constructed from materials such as cement concrete, grid pavers and asphalt concrete are called as rigid channels. 10. What is a prismatic channels? Channels which are constructed from materials such as concrete, masonry and metal can withstand erosion under all including most extreme conditions are called as non-erodible channels. 11. What is meant by most economical section? The most economical cross section of a channel gives the maximum discharge with a constant cross section. 12. Compute the hydraulic mean depth of a small channel 1m wide, 0.5m deep with water flowing at 2m/s. Hydraulic mean depth(m), D = cross sectional area of flow Top Width = 13. Define normal depth 0.5 x 2 2 = 0.5m For a given channel geometry, slope, roughness and a specified value of discharge, a unique value of depth occurs in a steady, uniform flow, it is called as normal depth and is denoted by y o. The normal depth is used to design artificial channels in a steady and uniform flow is computed from Manning s equation.

4 14. Write the Basin s formula for the discharge in the channel. Basin s formula: Chezy s constant, C = ( k R ) Where k is the Basin constant. 15. On what condition most economical trapezoidal channel section is derived? The most economical section of a trapezoidal channel is (a) Sloping side of cross section is equal to half the top width. (b) Angle of channel sides make with horizontal is 60 o. (c) Hydraulic radius is equal to half the depth of water. 16. Write down the formula for Froude number. Froude number, F = V gd < 1 Where V = Average velocity of flow in m/s g = Accelerarion doe to gravity (9.1 m 3 /sec) D = Hydraulic mean depth in m. 17. Write down the fundamental equations describe the open channel flow. The three fundamental equations that describes the flow of fluid which is derived from the fundamental law of physics are; (i) The continuity equation based on conservation of mass. (ii) The energy equation based on conservation of energy. (iii) The momentum equation based on conservation of momentum. 18. Define specific energy. Specific energy of a flowing liquid is defined as per unit weight of a liquid with respect to the bottom of the channel. It is denoted by the symbol E. E = y + v 2g Where Y = depth of flow V = velocity of flow 19. Define critical flow. The depth of flow at which the specific energy, E is minimum is called critical depth (y c ).

5 For rectangular channel critical depth, ` y c = ( q ) g 20. In an open channel of rectangular section if the minimum specific energy is 6m, what is its critical depth? E mimimum = 3 y c 2 Critical depth, y c = 2 3 Emin = 2 3 x 6 = 4m 21. Define transition depth. For rate of flow calculation, instead of reducing the width of channel, depth of water is lowered or increased to certain height by providing hump called transition depth. 22. Define specific force. Specific force is the sum of the pressure force (F) and momentum force due to flow (M) per unit weight of the liquid at a section. Where Specific force, F s = (F+M) γ ϒ = weight density of liquid 23. What are the factors considered while designing non-erodible channels? The following factors considered while designing the non-erodible channels as; (a) Manning s constant n value of the material (b) Channel slope (c) Free board 24. Write down the Manning s formula for determining velocity of flow in an open channel. Where V = 1 n R2/3 S 1/2 n = Manning s roughness coefficient. V = mean velocity of flow in m/s. R = Hydraulic radius of the channel in m. S = channel bed slope. 25. Write down the chezy s formula for determining velocity of flow in an open channel. V = C RS

6 Where C = Chezy s constant R = A P is the hydraulic mean radius. S = slope of the channel bed. PART B 1. Define specific energy of flow at a channel section. Draw the specific energy curve and explain. 2. A trapezoidal channel has side slopes of 1 horizontal to 2 vertical and the slope of the bed is 1 in The area of the section is 42 m2. Find the dimensions of the section if it is to be most economical. Determine the discharge of the most economical section of C = Describe various types of flow in an open channel. 4. A rectangular channel with a base width of 0.60 m carries a discharge of 100 lps. The Chezy's C is 60. If the depth of flow is 0.25 m, determine the bed slope of the channel 5. In a flow through a rectangular channel for a certain discharge froude number corresponding the two alternate depths are y1 and y2. show that (F2/F1) (3/2)=(2+F22)/(2+F12) 6. A rectangular channel 1.5m wide and depth 2.25m, discharge is 10m3/sec. calculate the specific energy and depth alternate to the given depth. 7. A trapezoidal channel has a bottom width 6m, and side slope of 2h to 1v if a depth of flow is 1.2m at a discharge of 10m3/sec. compute the specific energy and critical depth. 8. Define wide open channel and also what are the important assumptions in hydraulic parameters? 9. The rectangular channel carries a discharge of 30m3/sec. The bottom width of the channel is 6.0m and flow velocity is 1.75m/sec. Determine two alternate depths possible in the channel. 10. If y1 and y2 are alternate depths in a rectangular channel show that YC3 = (2y12y22) / (y1 + y2) and hence the specific energy E = (y12 + y1y2 + y22) / (y1 + y2) 11. For a constant specific energy of 3.0m, what maximum flow may occur in a rectangular channel of 4.5m bed width? 12. The specific energy for a 3m wide channel is 8N.m/N. What is the maximum possible discharge in the channel? 13. Show that in rectangular channel maximum discharges occurs when the flow is critical for a given value of specific energy. 14. The specific energy for a 5m wide rectangular channel is 4m, the discharge of water through the channel is 19cumecs. Determine the alternate depths of flow. 15. Show that the minimum specific energy in a rectangular channel is 1.5 times the critical depth. 16. Show that the relation between alternate depths y1 and y2 in a rectangular channel can be expressed by 2y12y2/(y1+y2)=yc3 where yc is the critical depth of flow. 17. For a constant energy of 2.4N.m/N. Calculate the maximum discharge that may occur in a rectangular channel 4m wide.

7 UNIT II GRADUALLY VARIED FLOW Dynamic equations of gradually varied and spatially varied flows - Water surface flow profile classifications: Hydraulic Slope, Hydraulic Curve - Profile determination by Numerical method: Direct step method and Standard step method, Graphical method - Applications. 1. Define varied flow. Explain its classification. Flow properties such as depth of flow, area of cross section and velocity of flow vary with respect to distance called non-uniform flow. It is also called varied flow. The varied flow is broadly classified into two types: (i) Rapidly varied flow (ii) Gradually varied flow 2. Define Spatially varied flow(svf) Flow varies with longitudinal distance called spatially varied flow. In steady varied flow, no flow is externally added to or taken out of the canal system and the discharge is constant at all sections. However, if some flow is added to or taken out from the flow system is known as Spatially varied flow. Examples: Lateral channel spillways, lateral weirs 3. Define gradually varied flow and rapidly varied flow in an open channel. Gradually varied flow occurs over long distance. Example: Back water in a dam Depth of water increases rapidly over a short length of the channel is called rapidly varied flow. Example: Hydraulic jump. 4. How spatially varied flow is classified based on discharge? Spatially varied flow can also be classified into two types; (i) Discharge increases with distance Lateral inflow (ii) Discharge decreases with distance Lateral outflow 5. Wite down the dynamic equation of gradually varied flow. Dynamic equation of gradually varied flow is given by

8 Slope of free water surface, dy dx = S Se Where, S e = slope of energy line S = Bed slope V = Velocity of flow D = Depth of flow 1 ( V gd ) 6. State the assumptions made in the derivation of dynamic equation for gradually varied flow. The following are the assumptions made for analyzing the gradually varied flow; (i) (ii) (iii) (iv) (v) The flow is steady. The pressure distribution over the channel section is hydrostatic, i.e., streamlines (Ѱ) are straight and parallel. The head loss is same as for uniform flow A channel is prismatic Roughness coefficient is constant along the channel length. 7. Classify surface profiles in a channel. Based on channel slopes, channels can be classified into five typed as; (i) (ii) (iii) (iv) (v) Mild slope (M) Critical slope (C) Steep slope (S) Horizontal slope (H) Adverse slope (A) 8. Write about backwater curves. The profile of the rising water on the upstream side of the dam is called back water curve. The distance along the bed of channel between sections where the water is having maximum height and at the point where the water starts rising up known as length of water curve. 9. Define draw-down curve. When the depth of flow decreases along the flow direction, slope of water surface (dy/dx) is negative and the surface profile is known as draw-down curve. 10. Write down the expression to determine the length of the backwater curve. Length of the backwater curve, L = E2 E1 S Se Where, E 2 = Energy head at section 2-2

9 E 1 = Energy head at section 1-1 S e = slope of energy line S = Slope of bed. 11. What is the normal slope of an open channel? denoted by S n. If the flow in the channel is uniform, the channel is said to have a normal slope 12. What are the flow profiles possible in mild sloped channels? (i) (ii) (iii) Flow behind an overflow weir Flow over a free overfall Flow downstream of a sluice gate 13. What are the methods used to determine the length of surface profile? methods: (i) (ii) (iii) Length of surface profile is determined with the help of any of the following Graphical Integration method Direct step method Standard step method 14. Define the term Afflux. Afflux is defined as the maximum increase in water level due to obstruction in the path of flow of water. 15. Show that maximization of discharge requires minimization of wetted perimeter of the channel for a given area of flow. For a given channel slope, roughness coefficient and area of flow, the maximum discharge of channel is obtained when the wetted perimeter is minimum. For wetted perimeter (P) to be minimum, dp dy = 0 If second derivative of P is positive, the condition of minimum P is obtained. PART - B 1. A canal is formed with side slopes 2:1 and a bottom width of 3.0m. The bed slope is 1 in Using manning s formula and assuming manning s n as Calculate the depth of water for a discharge of 3.0m3/sec for a uniform flow. 2. Determine the dimensions of the most economical trapezoidal channel with manning s N = 0.02, to carry a discharge of 14m3/sec at a slope of 4 in 10, Determine the longitudinal slope of a triangular channel carrying 1.2m3/sec for a normal depth of flow 0.75m and a side slope 2 : 1. Take chezy s C = 45.

10 4. A trapezoidal channel with side slope 1 to 1 has to be designed to convey 10m3/sec at a velocity of a 2m/sec so that the amount of concrete lining for the bed and sides is the minimum. Calculate the area of lining required for one metre length of channel 5. What diameter of a semicircular channel will have the same discharge has a rectangular channel of width 2.5m and depth 1.25m?.Assume the bed slope and Manning s n are the same for both the channels. 6. A canal is formed with side slopes 2:1 and a bottom width of 3.0m. The bed slope is 1 in Using manning s formula and assuming manning s n as 0.025, calculate the depth of water for a discharge of 3.0m3/sec for a uniform flow. 7. Obtain an expression for the depth of flow in a circular channel which gives maximum velocity for a given longitudinal slope. The resistance to flow can be expressed by manning's equation 8. In a rectangular channel 3.5m wide, flow depth of 2m, find how high can be raised without causing afflux. If the upstream depth of flow raised to 2.5m what should be the height of the hump? Flow in the channel is 26.67m3/sec. 9. Calculate the critical depth and corresponding specific energy for a discharge of 5.0m3/sec in the following channel. i) Rectangular channel of bedwidth 2.0m ii) Triangular channel of side slope 1h and.5v iii) Circular channel of diameter 2.0m 10. Prove that for maximum discharge in circular channel the depth of flow is equal to 0.95 times diameter of the channel. 11. A trapezoidal channel having bottom width 6m and side slope 2h and 1v is laid in the bottom slope of if it carries a uniform flow of water at the rate of 10m3/sec, compute the normal depth and the mean velocity of flow. Take mannings n as Define uniform flow in open channel and write chezy s equation. 13. The trapezoidal channel of bottom width of 3m side slope 1.5h and 1v carries discharge of 10m 3 /sec at a depth of 1.5m under uniform flow condition the longitudinal slope of channel is Compute manning s roughness coefficient of the channel 14. A circular pipe diameter 600mm carries discharge 0.2m3/sec will flow half full. Determine the slope of pipe to be laid in the ground. Assume manning s n=0.013 for concrete pipe. Also determine the depth of flow if the pipe is laid in a slope of Derive chezy s formulae to determine the velocity of flow in open channel. UNIT III RAPIDLY VARIED FLOW Application of the energy equation for RVF - Critical depth and velocity - Critical, Subcritical and Super-critical flow - Application of the momentum equation for RVF - Hydraulic jumps - Types - Energy dissipation - Surges and surge through channel transitions.

11 1. Differentiate the gradually varied flow and rapidly varied flow S.No Gradually varied flow Rapidly varied flow 1 Occurs over long distances. Example: Back water in a dam Depth of water increases rapidly over a short length of the channel. Example: Hydraulic jump 2 It is not always possible to have uniform depth across the flow It occurs when there is a change from super critical to subcritical flow 3 Pressure distribution is approximately hydrostatic In these regions, surface is highly curved and the assumptions of hydrostatic pressure distribution do not apply. 2. Define energy dissipation When the hydraulic jump takes place, a loss of energy occurs due to eddy formation and turbulence. This loss of energy or energy dissipation is equal to the difference of specific energies at two different sections. 3. What is the formula for power lost by energy dissipation? Power lost by energy dissipation in kw = gqh L Where g = Acceleration due to gravity (9.81 m/s 2 ) Q = Rate of flow in m 3 /s. h L = Head in m. 4. Why momentum equation only used for rapidly varied flow problems. Generally, the hydraulic jump occurs at the downstream side of a surplus weir, when a super critical flow and a sub critical flow meet. Both the flows join in an extremely turbulent manner which causes large energy losses because the large energy losses the energy equation cannot be used for analysis. However, the momentum equation can be used for hydraulic jump analysis. 5. What is hydraulic jump in horizontal bed channel? The rise of water level which takes place due to the transformation of the shooting into the streaming flow is known as hydraulic jump. 6. Write the expression for hydraulic jump? where y 2 = y 1 2 ( 1 + 8(F 1)2-1)

12 Depth of hydraulic jump = y 1 y 2 y 1 = Depth of flow at section 1-1 y 2 = Depth of flow at section 2-2 F 1 = Froude number at section Define loss of energy due to hydraulic jump. h L = (y2 y1) 4y1y2 where y 1 = Depth of flow at section 1-1 y 2 = Depth of flow at section Give the relationship between length and depth of hydraulic jump. From experiments, for a rectangular channel, the length of hydraulic jump is equal to 5 to 7 times the height of the hydraulic jump. L = 5 to 7 (y 2 y 1 ) 9. State the uses of hydraulic jump. The kinetic energy of the flow after the hydraulic jump is greatly reduced which may prevent the erosion of channel boundaries of downstream side. 10. What is the state of flow after the formation of a hydraulic jump? Streaming or tranquil flow occurs after the formation of hydraulic jump. Shooting or supercritical flow is an unstable flow and it does not continue on the downstream side of a surplus weir. Then this shooting will convert itself into a streaming or tranquil flow and hence, the depth of water will increase. 11. What are the conditions for the formation of hydraulic jump? (i) When the depth of flow is forced to change from a supercritical depth to a subcritical depth. (ii) Froude number decreases from >1.0 to <1.0 (iii) Jump will not occur when Froude number is <1.0 (iv) Jump does not occur from subcritical to supercritical flow only 12. Explain the classification of hydraulic jumps. Based on Froude number (F), hydraulic jump can be classified as; (a) Undulation jump: F ranges from 1 to 1.7 (b) Weak jump: F ranges from 1.7 to 2.5

13 (c) Oscillating jump: F ranges from 2.5 to 4.5 (d) Steady jump: F ranges from 4.5 to 9.0 (e) Strong jump: F ranges from greater than What are surges? surge. When the properties such as discharge or depth varying suddenly, it is called Example: Sudden closure of gate. 14. What is meant by positive and negative surges? (i) (ii) Positive surge A surge producing increases in depth Negative surge A surge producing decrease in depth 15. What is transition in open channel? Transition means a change of channel cross section. (i) (ii) Provision of a hump or depression along depth Contraction or expansion of channel width, in any combination. 16. Write down the applications of transition Transition in open channel flow is made to measure discharge of channel. Generally, discharge Q = area(a) x velocity(v). for discharge calculation, both cross section of flow and velocity are necessary. With the help of channel transition, the discharge of water is obtained from measured flow cross section dimensions and specific energy equations. Part B 1. A rectangular channel of width 5m flows 1.5m in uniform flow bed slope of channel is The uniform flow is blocked be a weir and flow depth of 4m from bed of the channel. Determine the length of the back water profile between 4m to 2m. use direct step method and assume manning s n as Discuss briefly the types of hydraulic jump, its application 3. Explain the development of M, S and H profiles with neat sketches 4. Briefly explain the direct step method and standard step method to determine the gradually varied flow profiles. 5. Derive the dynamic equation of gradually varied flow. 6. Determine the slope of the free water surface in a rectangular channel of width 20m, having depth of flow 5m. the discharge through the channel is 52 cumecs. The bed slope of the channel is 1 in 4000.Assume chezy s constant c as During an experiment conducted on a hydraulic jump, in a rectangular open channel 0.5m wide, the depth of water changes from 0.2m to 0.5m. Determine the discharge in the channel and the loss of head due to the formation of hydraulic jump. 8. Derive the expression for loss of energy in a hydraulic jump.

14 9. Explain the direct step method for computing the length of the water surface profile. 10. State the application of hydraulic jump. 11. A partially open sluice gate discharges water at 10m/sec with 1m depth in a horizontal rectangular channel of width 5m. can a hydraulic jump occur. If so find the sequent depth and energy loss. 12. Define uniform flow and draw the hydraulic gradient line, total energy lice and water surface for uniform flow. 13. A concrete lined trapezoidal channel (n=0.015) is to have a side slope of 1 horizontal to 1 vertical. The bottom slope is to be Find the bottom width of the channel necessary to carry 100m 3 /sec of discharge at a normal depth of 2.5m. 14. A rectangular channel 10m wide carries a discharge of 30m3/s. it is laid at a slope of if at a section in this channel, the depth is 1.6m, how far upstream or downstream from the section will the depth be 2.0. Take manning s n as A horizontal rectangular channel 4m wide carries a discharge of 16m3/sec. determine whether a jump may occur at an initial depth of 0.5m or not. If jump occurs determine the sequent depth to this initial depth. UNIT IV TURBINES Impact of Jet on vanes - Turbines - Classification - Reaction turbines - Francis turbine, Radial flow turbines, draft tube and cavitation - Propeller and Kaplan turbines - Impulse turbine - Performance of turbine - Specific speed - Runaway speed - Similarity laws. 1. What is hydraulic turbine? Hydraulic turbines are the machines which convert the energy of flowing water into mechanical energy. 2. What are the Classification of turbines? Based on action of the water flowing: (i) Impulse turbine (ii) Reaction turbine Based on the main direction of water flow: (i) (ii) (iii) (iv) Tangential flow turbine Radial flow turbine Axial flow turbine Mixed flow turbine Based on the head and quantity of water required:

15 (i) High head turbine (ii) Medium head turbine (iii) Low head turbine 3. Classify hydraulic turbines based on specific speed and head. Head and quantity basis: (i) High head turbine (ii) Medium head turbine (iii) Low head turbine Specific speed basis: (i) Low specific speed (ii) Medium specific speed (iii) High specific speed 4. What is impulse turbine? Give an example. In impulse turbine, all the energies are converted into kinetic energy. From these, the turbine will develop high kinetic energy power. This turbine is called impulse turbine. Example: Pelton turbine 5. What is radial flow turbine? In the turbine, the water flows along the radial direction and mainly in the plane normal to the axis of rotation as it passes through the runner. It may be an either inward radial flow type or outward radial flow type. 6. What are reaction turbines? Give examples. In a reaction turbine, the runner utilizes both potential and kinetic energies. Here, the portion of potential energy is converted into kinetic energy before entering into the turbine. Example: Francis turbine, Kaplan turbine 7. Differentiate the impulse and reaction turbine. S.No Impulse turbine Reaction turbine 1 All potential energies are converted into kinetic energy by nozzle before entering to turbine runner. Only a portion of the fluid energy is transferred into kinetic energy before the fluid enters the turbine 2 Blades are only in action when they Blades are in action at all time are in front of nozzle 3 Flow regulation is possible without Flow regulation is possible with loss

16 loss 4 Wheel does not run full and air has free access to the buckets Water completely fills the vane passages throughout the operation of the turbine 8. Differentiate Francis and Kaplan turbine. S.No Francis turbine Kaplan turbine 1 Correct disposition of the guide and moving vanes is obtained at full load Correct disposition of the guide and moving blades are obtained at only load only 2 System may have one or two servomotors depending on the size Two servomotors respective of the size of the unit always do governing of the unit 3 Since the guide vanes are only controlled high efficiency is obtained In both guide and runner vanes, high efficiency is obtained even at partial loads 4 Servomotors are kept outside the shaft Both the servomotors are kept inside the hollow shaft of the turbine runner 9. What is the purpose of providing a casing in turbine? A casing is made of cast iron or fabricated steel. It is used to prevent the splacing of water and discharge water to tailstock. It also acts as a safeguard against accidents. 10. What is a draft tube? In which type of turbine it is mostly used? The tube which increases the outlet velocity of turbines is known as draft tube. So, the head is saved by fitting draft tube. 11. What are the types of draft tube? (i) Straight conical or concentric tube (ii) Elbow type 12. Why draft tubes not used in impulse turbine? It is an integral part of low head turbines with large amount of flow but impulse turbines are high head turbines. So, it is not needed to use in impulse turbines. 13. What is overall efficiency in turbines? It is defined as the ratio of power available at the turbine shaft to the power available from the water jet.

17 shaft power ἠ = = P water power wqh 14. What are unit quantities in a turbine? Unit quantities refer to the turbine parameters which are obtained for a particular turbine operated under a unit head. For estimating unit quantities, it is assumed that the efficiency of the turbine remains unchanged. The velocity triangles under the actual working head and any other assumed head are to be similar. 15. Define unit speed of turbine. Unit speed is defined as the speed of turbine when working under a unit head. Unit speed, N u = N/ H 16. Define the specific speed of a turbine. Specific speed is the speed of a geometrically similar turbine (I.e., a turbine identical in shape, dimensions, blade angles and gate opening etc ) which will develop unit power while working under unit head. 17. What is meant by surge tank? What is the purpose of providing surge tank? reduce. A surge tanak is a small reservoir or tank in which the water level rises or falls to Purpose: To reduce the rapid velocity fluctuation in a pipeline during start-up and shutdown of a turbine. 18. Define cavitation. Cavitation is defined as the phenomenon of formation of vapour bubbles of a flowing liquid in a region where the pressure of the liquid falls below its vapour pressure and the sudden collapsing of these vapour bubbles in a region of higher pressure. 19. What is meant by governing of turbines? The method of maintaining the speed of the turbine is constant irrespective of variation of the load on the turbine known as governing of turbines. The governors regulate the supply of fluid to the turbine in such a way that the speed of the turbine is constantly maintained as far as possible under varying load conditions. The principal method of hydraulic turbine governing is throttle governing or centrifugal governing. 20. What is negative slip in reciprocating turbine? It is defined as the turbine turning the shaft and the first stator winding and the first armature operate as an exciter for supplying excitation to the rotating field winding of a main generator.

18 PART B 1. Determine the speed of a pelton wheel, its diameter, number of jet required and the size of each jet if it develops 13,800 MHP under a head 0f 430m. Its specific speed is 42. Assume necessary suitable values. 2. Explain the working of radial flow turbine with neat sketch. 3. Distinguish between impulse and reaction turbines. 4. Derive an expression for specific speed of a turbine. 5. Prove that the maximum efficiency is only 50%. When a liquid jet strikes a series a flat vanes mounted on the periphery of a wheel. 6. A reaction turbine works at 450 rpm under a head of 120m. The diameter at inlet is 120 cm and the flow area is 0.4m 2. The angles made by absolute and relative velocities at inlet are 20 and 60 respectively with the tangential velocity. Find i) discharge ii) power developed and iii) hydraulic efficiency. Assume velocity of whirl at outlet is zero. 7. What is the main advantage of fitting draft tube in francis turbine? 8. The velocity of whirl at inlet to the runner of an inward flow reaction turbine is 3.15 H m/sec and the velocity of flow at inlet is 1.05 H m/s. the velocity of whirl at exit is 0.22 H m/s in the same direction as at inlet and the velocity of flow at exit is 0.83 H m/s, where H is head of water 30m. The inner diameter of the runner is 0.6 times the outer diameter. Assuming hydraulic efficiency of 80%. Compute angle of the runner vanes at inlet and exit. 9. A impulse wheel has a mean bucket speed of 10 m/s with a jet of water flowing at the rate of 1.0m 3 /s under a head of 50m. The buckets deflects the jet through an angle of 165 degree. Calculate the power given by water to the runner and the hydraulic efficiency of the turbine. Assume coefficient of velocity as The external and internal diameters of an inward flow reaction turbine are 1.2m and 0.6 respectively. The head on the turbine is 22m and velocity of flow through the runner is constant and is equal to 2.5m/s. the guide blade angle is 10 degree and the runner vanes are radial at inlet. The discharge is radial at outlet. Determine i) the speed of the turbine ii) the vane angle at outlet iii) hydraulic efficiency 11. What are the main components of Kaplan turbine? Explain with a neat sketch. 12. A Kaplan turbine is to be designed to develop 9000 kw. The net available head is 5.6m. the speed ratio is 2.09 and the flow ratio is The overall efficiency is 86% and the diameter of the boss is one third the diameter of the runner. Determine the diameter of the runner, speed and specific speed of the turbine. 13. Classify hydraulic turbines. 14. A pelton wheel has to work under a head of 60m while running at 200 rpm. The turbine is to develop a power of kw. The velocity of buckets is 0.45 times of the velocity of jet. The overall efficiency is 0.80 and coefficient of velocity is Design the pelton wheel. 15. A Kaplan turbine while working under a head of 35m develops power of 20,000kW. Assume flow ratio of 0.6, speed ratio of 2, the diameter of boss is 0.35times the diameter of the runner and overall efficiency is 85%. Find the diameter, speed and specific speed of the turbine

19 UNIT V PUMPS Centrifugal pumps - Minimum speed to start the pump - NPSH - Cavitations in pumps - Operating characteristics - Multistage pumps - Reciprocating pumps - Negative slip - Flow separation conditions - Air vessels, indicator diagrams and its variations - Savings in work done - Rotary pumps: Gear pump. 1. Differentiate pump and turbine S.No Pump Turbine 1 Energy absorbing device Energy producing device 2 Mechanical energy is converted into hydraulic energy to increase the pressure of fluid and transfer to other systems Hydraulic energy is converted into mechanical energy to produce energy 2. List the types of impellers and casings for a centrifugal pump. Impellers: (i) Shrouded or closed impeller (ii) Semi open type impeller (iii) Open impeller Casing: (i) Volute casing (ii) Vortex casing (iii) Volute casing with guide blades 3. What is meant by priming of pumps? The delivery valve is closed and the suction pipe, casing and portion of the delivery pipe up to delivery valve are completely filled with the liquid so that no air pocket is left called as priming. 4. What is NPSH? It is Net Positive Suction Head that combines absolute pressure at inlet to pump, vapour pressure head of liquid and velocity head in suction pipe. Net positive suction head = Absolute head vapour pressure head + velocity head NPSH = ((p a /w) (p v /w) h s h fs )

20 5. Define specific speed of pump The specific speed of a centrifugal pump is defined as the speed of a geometrically similar pump which will deliver unit quantity (i.e., 1 litre per second) against a unit head (i.e., 1 meter). 6. Write the equation for specific speed for pumps and turbines. Specific speed of pumps, N s = (N P)/ H 5/4 m Specific speed of turbins, N s = (N Q)/ H 3/4 m Where N= speed of the turbine or pump P= Power developed Q= discharge H m = Manometric head. 7. What is meant by multistage pump? The flow rate or head of fluid obtained is not enough with one pump. So, multiple pumps have to be used. In order to increase either flow rate or head of discharge, pumps are connected in series or parallel. 8. Define cavitation in pumps Cavitation is defined as the phenomenon of formation of vapour bubbles of a flowing liquid in a region where the pressure of the liquid falls below its vapour pressure and the sudden collapsing of these vapour bubbles in a region of higher pressure. 9. State any two precaution against cavitation (i) The pressure should not be allowed to fall below its vapour pressure (ii) Special material coatings can be given to the surfaces where the cavitation occurs. 10. Define suction and delivery strokes. Suction stroke is when the crank rotates clockwise from inner dead centre(idc) to outer dead centre(odc), the piston moves outward to the right and a vacuum is created on the left side of the piston. Delivery stroke is when the crank rotates from ODC to IDC, the piston moves inward to left and a high pressure is built up in the cylinder. 11. Define slip of reciprocating pump. When does the negative slip occur? The difference between theoretoical discharge and actual discharge is called slip of the pump.

21 Slip = Q th Q act Percentage slip = (Q th Q act )/ Q th x Distinguish between centrifugal and reciprocating pump. S.NO Centrifugal pump Reciprocating pump 1 Pumps work under the principle of centrifugal action Pumps work under the reciprocating action 2 Impellers and casings are used Piston and cylinder are used 13. Define negative slip. How does it occur? In most of the cases, Q act is less than than Q th. But in some times, Q act may be higher than Q th. In such cases, c d is greater than unity and the slip will be negative. In that case, the slip pof the pump is known as negative slip. Negative slip is possible, when the delivery pipe is short, suction pipe is long and pump is running at high speed. 14. What is indicator diagram? Indicator diagram is a graph plotted between head in the cylinder and distance traveled by piston from inner dead centre for one complete revolution of the crank. 15. What is an air vessel? State its functions. An air vessel is a closed chamber made of cast iron. It is used to provide uniform discharge from reciprocating pump. It has opening at its base through which the water flows into the air vessel or from the vessel depending on the quantity of water inside the cylinder. 16. What are the advantages of fitting air vessels in a reciprocating pump? (i) The possibility of cavitation can be reduced (ii) The pump can be run at higher speed for the given minimum pressure head (iii) Suction pipe length can be increased 17. What is the function of foot valve in a pump? The foot valve is a one-way valve located above the strainer into the suction pipe. It is used to fill the pump with liquid, before it is started (i.e., priming_0 and it prevents back when the pump is stopped. PART - B 1. The centrifugal pump has the following characteristics. Outer diameter of impeller is 800mm: width of the impeller vane at outlet = 100mm: angle of the impeller vanes at outlet is 40

22 degree. The impeller runs at 550 rpm and delivers 0.98m3/sec under an effective head of 35m. A 500kW motor is used to drive the pump. Determine the manometric, mechanical and overall efficiencies of the pump. Assume water enters the impeller vanes radially at inlet. 2. A single acting reciprocating pump discharges 5l / sec with cylinder bore diameter 200mm and its stroke length 300mm. The pump runs at 350rpm and lifts water through a height of 25m. The delivery pipe is 30m long and 100 mm in diameter. Find the theoretical discharge and theoretical power required to run the pipe and determine the percentage slip and also determine the delivery head due to acceleration at beginning, middle and end 3. Distinguish between single stage pump and multistage pump. 4. The diameters of a impeller of a centrifugal pump at inlet and outlet are 300mm and 600mm respectively. Determine the minimum starting speed of the pump of it work against head of 28m. 5. Explain the working principle of single acting reciprocating pump with neat sketch. 6. A single acting reciprocating pump running at 50rpm delivers 0.01m3/sec of water. The diameter of the plunger is 200 mm and the stroke length is 400mm. the delivery and suction head are 10m and 5m respectively. Determine the theoretical discharge, slip, percentage slip, coefficient of discharge and the power required to derive the pump. 7. Define manometric efficiency and net positive suction head (NPSH). 8. A centrifugal pump works against a net head of 20m at a speed of 1200rpm. The vane angle at Outlet is 30deg the empeller diameter and with at outlet are 40cm and 6cm respectively. Find the discharge.take manometric efficiency as 95%. 9. Explain the working of single acting reciprocating pump with air vessel. 10. A single acting reciprocating pump running at 30rpm has a stroke length of 40cm and piston Diameter of 20cm. the suction head is 3.0m and length and diameter of suction pipe are 6m and 10cm respectively. Take f=0.02 and Hatm=10.3m of water. Find the absolute pressure head nside the cylinder at the beginning middle and end of suction stroke. 11. What is breaking jet in pelton wheel turbine? 12. A pelton wheel has a mean bucket speed of 10m/s with a jet of water flowing at the rate of 0.7m3/s under a head of 30m. the buckets deflects the jet through an angle of 160 degree. Calculate the power given by water to the runner and the hydraulic efficiency of the turbine. Assume coefficient of velocity as What is specific speed of a pump and what is its importance? 14. The cylinder bore diameter of a single acting reciprocating pump is 150mm. and its stroke length is 300 mm. the pump runs at 50 rpm and lifts water through a height of 25m. the delivery pipe is 22m long and 100mm in diameter. Find the theoretical discharge and the theoretical power required to run the pump. If the actual discharge is 4.2 litres/s,find the percentage slip. 15. The inlet and outlet diameter s of the impeller of a centrifugal pump are 25cm and 50 cm respectively. The velocity of flow at outlet of flow is 2.5m/s and the vanes are set back at an angle of 45deg at the outlet. Find the minimum starting speed if the manometric efficiency is 0.8.