Fluid Mechanics Question Bank Ce8394

CE8394 - Fluid Mechanics and Machinery 2018-2019

CE8394

Mechanical Engineering

FLUID MECHANICS AND MACHINERY

LT PC 3003

OBJECTIVES: 

The applications of the conservation laws to flow through pipes and hydraulic machines are studied



To understand the importance of dimensional analysis.



To understand the importance of various types of flow in pumps and turbines.

UNIT I FLUID PROPERTIES AND FLOW CHARACTERISTICS 8 Units and dimensions- Properties of fluids- mass density, specific weight, specific volume, specific gravity, viscosity, compressibility, vapor pressure, surface tension and capillarity. Flow characteristics – concept of control volume - application of continuity equation, energy equation and momentum equation. UNIT II FLOW THROUGH CIRCULAR CONDUITS 8 Hydraulic and energy gradient - Laminar flow through circular conduits and circular annuli-Boundary layer concepts – types of boundary layer thickness – Darcy Weisbach equation –friction factor- Moody diagramcommercial pipes- minor losses – Flow through pipes in series and parallel. UNIT III DIMENSIONAL ANALYSIS 9 Need for dimensional analysis – methods of dimensional analysis – Similitude –types of similitude Dimensionless parameters- application of dimensionless parameters – Model analysis. UNIT IV PUMPS 10 Impact of jets - Euler‟s equation - Theory of roto-dynamic machines – various efficiencies– velocity components at entry and exit of the rotor- velocity triangles - Centrifugal pumps– working principle - work done by the impeller - performance curves - Reciprocating pump- working principle – Rotary pumps – classification. UNIT V TURBINES 10 Classification of turbines – heads and efficiencies – velocity triangles.Axial, radial and mixed flow turbines.Pelton wheel, Francis turbine and Kaplan turbines- working principles - work done by water on the runner – draft tube. Specific speed - unit quantities – performance curves for turbines –governing of turbines. TOTAL:

45

PERIODS OUTCOMES: 

Upon completion of this course, the students can able to apply mathematical knowledge to predict the properties and characteristics of a fluid.



Can critically analyse the performance of pumps and turbines.

TEXT BOOK: 1. Modi P.N. and Seth, S.M. "Hydraulics and Fluid Mechanics", Standard Book House, New Delhi 2004. REFERENCES: 1. Streeter, V. L. and Wylie E. B., "Fluid Mechanics", McGraw Hill Publishing Co. 2010 2. Kumar K. L., "Engineering Fluid Mechanics", Eurasia Publishing House(p) Ltd., New Delhi 2004 3. Robert W.Fox, Alan T. McDonald, Philip J.Pritchard, “Fluid Mechanics and Machinery”, 2011. 4. Graebel. W.P, "Engineering Fluid Mechanics", Taylor & Francis, Indian Reprint, 2011 St.Joseph’s College of Engineering

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CE8394 - Fluid Mechanics and Machinery 2018-2019

Mechanical Engineering

ANNEXURE I (A) PROGRAM OUTCOMES (POs) Engineering graduates will be able to: 1. Engineering knowledge: Apply the knowledge of mathematics, science, engineering fundamentals, and an engineering specialization to the solution of complex engineering problems. 2. Problem analysis: Identify, formulate, review research literature, and analyze complex engineering problems reaching substantiated conclusions using first principles of mathematics, natural sciences, and engineering sciences. 3. Design/development of solutions: Design solution for complex engineering problems and design systems components or process that meet the specified needs with appropriate consideration for the public health and safety, and the cultural, societal, and environmental considerations. 4. Conduct investigations of complex problems: Use research-based knowledge and research methods including design of experiments, analysis and interpretation of data, and synthesis of the information to provide valid conclusions. 5. Modern tool usage: Create, select, and apply appropriate techniques, resources, and modern engineering and IT tools including prediction and modeling to complex engineering activities with an understanding of the limitations. 6. The engineer and society: Apply reasoning informed by the contextual knowledge to assess societal, health, safety, legal and cultural issues and the consequent responsibilities relevant to the professional engineering practice. 7. Environment and sustainability: Understand the impact of the professional engineering solutions in societal and environmental contexts and demonstrate the knowledge of, and need for sustainable development. 8. Ethics: Apply ethical principles and commit to professional ethics and responsibilities and norms of the engineering practice. 9. Individual and team work: Function effectively as an individual, and as a member or leader in diverse teams, and in multidisciplinary settings. 10. Communication: Communicate effectively on complex engineering activities with the engineering community and with society at large, such as, being able to comprehend and write effective reports and design documentation, make effective presentations, and give and receive clear instructions. 11. Project management and finance: Demonstrate knowledge and understanding of the engineering and management principles and apply these to one’s own work, as a member and leader in a team, to manage projects and in multidisciplinary environments. 12. Life-long learning: Recognize the need for, and have the preparation and ability to engage in independent and life-long learning in the broadest context of technological change. (B) PROGRAM EDUCATIONAL OBJECTIVES (PEOs) Engineering graduates will be able to A. Practice mechanical engineering in a broad range of industries both core engineering and non-engineering fields such as medicine, space, law or business. B. Pursue advanced education, research and development, and other creative and innovative efforts in science, engineering, and technology, as well as other professional careers. C. Conduct them in a responsible, professional, and ethical manner and attain professional maturity with deep understanding of the impact of the technological solutions in a societal and global context and a need for sustainable development. D. Participate as leaders in their fields of expertise and in activities that support service and economic development nationally and throughout the world. (C) PROGRAM SPECIFIC OBJECTIVES (PSOs) PSO 1: The students graduating in Mechanical Engineering will have profound foundation in mathematical, scientific and engineering domains necessary to achieve professional and productive excellence in technical and non-technical problem solving and analyzing engineering problems. PSO 2: The students graduating in Mechanical Engineering will have the ability to synthesize the engineering data and apply scientific principles for applications involving mechanical engineering using high end CAD/CAM/CAE computational packages such as CATIA, ANSYS and MATLAB. PSO 3:

St.Joseph’s College of Engineering

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CE8394 - Fluid Mechanics and Machinery 2018-2019

Mechanical Engineering

The students graduating in Mechanical Engineering will have the ability to pursue advanced careers and discharge his/her duties entrusted with high degree of commitment to address professional and ethical responsibilities, including a respect for diversity and provide cost effective engineering solutions.

COURSE OUTCOMES On completion of this course, the student will be able: CO304.1 1. To understand the basics concepts of fluid properties and their applications. CO304.2

2. To gain the fundamental knowledge on fluid flow through pipes of various section and its losses and boundary layer concept.

CO304.3

3. To formulate equations for model and prototype for various applications and analysing it dimensionally.

CO304.4

4. To understand the working principle of various pumps and its performance evaluation and comparison.

CO304.5

5. To understand the working principle of various turbine and its performance evaluation and comparison.

PO2

PO3

PO4

PO5

PO6

PO7

PO8

PO9

PO10

PO11

PO12

PSO1

PSO2

CO304.1

3

3

2

2

1

1

1

-

-

2

1

3

3

2

2

CO304.2

3

3

3

3

1

1

1

-

-

2

1

3

3

3

2

CO304.3

3

3

3

3

2

1

2

1

-

2

2

3

3

3

3

CO304.4

3

3

3

3

1

2

3

-

-

3

2

3

3

3

2

CO304.5

3

3

3

3

1

2

3

-

-

3

2

3

3

3

2

RELATION BETWEEN COURSE CONTENT WITH Cos UNIT I FLUID PROPERTIES AND FLOW CHARACTERISTICS S.No

Knowledge Level

Course Outcomes

Topics

1

U, An,Ap

Units and dimensions

CO304.1

2

U, Ap

Properties of fluids

CO304.1

3

U, An, Ap, E

Flow characteristics

CO304.1

4

U, An, Ap

concept of control volume

CO304.1

5

U, An, Ap, E

application of continuity equation

CO304.1

6

U, An, Ap, E

energy equation and momentum equation.

CO304.1

St.Joseph’s College of Engineering

3

PSO3

CE8394

PO1

MAPPING BETWEEN CO, PO AND PSO WITH CORRELATION LEVEL 1/2/3

CE8394 - Fluid Mechanics and Machinery 2018-2019

Mechanical Engineering

1

UNIT II FLOW THROUGH CIRCULAR CONDUITS Knowledge Course Topics Level Outcomes U, An Hydraulic and energy gradient CO304.2

2

U, An

Laminar flow through circular conduits

CO304.2

3

U, An, Ap

Boundary layer concepts

CO304.2

4

U, An, E

Losses in pipes

CO304.2

5

U, An, E

Flow through pipes in series and parallel

CO304.2

S.No

UNIT III DIMENSIONAL ANALYSIS Knowledge Level

S.No

Course Outcomes CO304.3

Topic

1

U

Need for dimensional analysis

2

U, An, Ap, E

methods of dimensional analysis

CO304.3

3

U, An

Similitude

CO304.3

4

U, An

Dimensionless parameters

CO304.3

5

U, An, Ap, E, C

Model analysis

CO304.3

UNIT IV PUMPS

1

Knowledge Level U, An, Ap

Euler‟s equation

Course Outcomes CO304.4

2

U, An, Ap

velocity triangles

CO304.4

3

U, An, E

Centrifugal pumps

CO304.4

4

U, An, E

Reciprocating pumps

CO304.4

5

U, An, E

Rotary pumps

CO304.4

S.No

Topic

UNIT V TURBINES S.No

Knowledge Level

Course Outcomes

Topic

1

U

Classification of turbines

CO304.5

2

U, An, Ap

velocity triangles

CO304.5

3

U, An, E

Axial, radial and mixed flow turbines

CO304.5

4

U, An, E

Pelton wheel, Francis turbine and Kaplan turbines

CO304.5

5

U, An, E

performance curves for turbines

CO304.5

6

U, An, Ap, E

governing of turbines

CO304.5

Ap – Apply; An – Analyze; U – Understand, E- Evaluate,C-Create St.Joseph’s College of Engineering

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CE8394 - Fluid Mechanics and Machinery 2018-2019

Mechanical Engineering

UNIT- I FLUID PROPERTIES AND FLOW CHARACTERISTICS PART – A 1. Define fluids. Fluid may be defined as a substance which is capable of flowing. It has no definite shape of its own, but confirms to the shape of the containing vessel. 2. What are the properties of ideal fluid? Ideal fluids have following properties It is incompressible; It has zero viscosity; Shear force is zero 3. What are the properties of real fluid? Real fluids have following properties i)It is compressible; ii) They are viscous in nature; iii) Shear force exists always in such fluids. 4. Define density and specific weight. Density is defined as mass per unit volume (kg/m3) Specific weight is defined as weight possessed per unit volume (N/m3) 5. Define Specific volume and Specific Gravity. Specific volume is defined as volume of fluid occupied by unit mass (m3/kg) Specific gravity is defined as the ratio of specific weight of fluid to the specific weight of standard fluid. 6. Define Surface tension and Capillarity. Surface tension is due to the force of cohesion between the liquid particles at the free surface. Capillary is a phenomenon of rise or fall of liquid surface relative to the adjacent general level of liquid. 7. Define Viscosity and what is the effect due to temperature on liquid and gases. (Apr/May 2017) It is defined as the property of a liquid due to which it offers resistance to the movement of one layer of liquid over another adjacent layer. The temperature has predominant effect on the viscosity of the liquids and gases. With the increase in temperature, the viscosity of liquid decreases rapidly whereas for gases it increases rapidly. 8. Define kinematic viscosity. It is defined as the ratio of dynamic viscosity to mass density. (m²/sec) 9. Define Relative or Specific viscosity. It is the ratio of dynamic viscosity of fluid to dynamic viscosity of water at 20°C. 10. Define Compressibility. It is the property by virtue of which fluids undergoes a change in volume under the action of external pressure.

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Mechanical Engineering

11. Define Newton’s law of Viscosity. (Nov/Dec 2012) According to Newton’s law of viscosity the shear force F acting between two layers of fluid is proportional to the difference in their velocities du and area A of the plate and inversely proportional to the distance between them. 12. What is cohesion and adhesion in fluids? Cohesion is due to the force of attraction between the molecules of the same liquid. Adhesion is due to the force of attraction between the molecules of two different liquids or between the molecules of the liquid and molecules of the solid boundary surface. 13. State momentum of momentum equation? It states that the resulting torque acting on a rotating fluid is equal to the rate of change of moment of momentum 14. What is momentum equation? (Nov/Dec 2012) It is based on the law of conservation of momentum or on the momentum principle. It states that, the net force acting on a fluid mass is equal to the change in momentum of flow per unit time in that direction. 15. Why is it necessary in winter to use lighter oil for automobiles than in summer? To what property does the term lighter refer? The term lighter refers to the property called viscosity. In winter, if heavy oil is used for automobiles, the oil becomes more viscous, and doesn’t serve lubrication purpose. So lighter oil is used. 16. If the pressure on the fluid is increased from 75 bar to 140 bar, the volume of liquid decreases by 0.15%. Find the bulk modulus of elasticity of the liquid. K 

dp   dV     V 

4.33 x 109 N/m2

17. At a certain point in flowing caster oil, the shear stress is 2 N/m 2 and velocity gradient is 0.25/sec. The mass density of the oil is 800kg/m3. Find the kinematic viscosity of oil in stokes.  

du dy



2  8 Ns / m 2 0.25

 

 1  m2 / s  100

18. State Pascal’s law. This law indicates that the pressure intensity at any point in a static liquid is equal in alldirections. 19. Does viscosity vary with pressure and temperature?(Nov/Dec 2013, May/June 2016, Nov/Dec 2016) The value of μ of liquid or gas is practically independent of pressure for the range generally countered in practice but it varies widely with temperature. The temperature has predominant effect on the viscosity of the liquids. With the increase in temperature, the viscosity decreases rapidly. St.Joseph’s College of Engineering

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Mechanical Engineering

20. State momentum of momentum equation? It states that the resulting torque acting on a rotating fluids equal to the rate of change of moment of momentum. 21. What is momentum equation? It is based on the law of conservation of momentum or on the momentum principle. It states that, the net force acting on a fluid mass is equal to the change in momentum of flow per unit time in that direction. 22. What is importance of kinematic viscocity?(Nov/Dec 2015) Since the density is a strong function of pressure and temperature, so is the kinematic viscosity. It is generally a preferred unit when we deal with motion of fluid under the influence of gravity and so forth 23.Define incompressible fluid. (Nov/Dec 2015) Compressibility is the property by virtue of fluid do not undergoes change in volume under the action of external pressure. 24. Calculate mass density and specific volume of 1 litre of liquid which weighs 7N. (Apr/May 2015) mass density = mass/volume = [7/9.810]/10-3 kg/m3 specific volume = volume/mass = 1/density 25. What is the use of control volume (Apr/May 2015) The region in which the mass crosses the system boundary is called control volume. A control volume is a mathematical abstraction employed in the process of creating mathematical models of physical processes. 26. how does a rewood viscometer work ? (May/June 2016) A Redwood viscometer is another efflux type viscometer, it has a vertical cylindrical chamber filled with liquid whose viscosity is to be measured. It is surrounded by a constant temperature bath and a capillary tube is attached vertically at the bottom of the chamber. For measurement of viscosity, liquid is allowed to flow through an orifice,and time for 50ml of liquid is noted and named as redwood seconds. So, the value of viscosity of the liquid may be obtained by comparison with value of time for the liquid of known viscosity. ν = 0.002t – (1.8/t) 27. Calculate the capillary rise in a glass tube of 2.5 mm diameter, when immersed in (i)water, and (ii)mercury.Take surface tension σ = 0.0725 N/m for water and σ = 0.52 N/m for a mercury in contact with air. The specific gravity of mercury is given as 13.6 and angle of contact 130 o ( Nov/Dec 2016&Apr/May 2017) (i) water: h = 4σ/wd = (4 x 0.0725)/ (9810 x0.0025) = 0.0118 m (ii) Mercury: h = 4σcosβ/wd = (4 x 0.52 x cos 130°)/ (13.6 x 9810 x 0.0025) = -0.004 m St.Joseph’s College of Engineering

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Mechanical Engineering

28.Brief on consequences of pascal’s law. (Nov/Dec 2017) When gravity is taken into account, Pascal’s law is to be modified. If the effect of gravity is neglected, then the pressure at one point will be equal to the pressure at another point. But, if force due to gravity is taken into account, then they are not equal. As the liquid column is in equilibrium, the forces acting on it are balanced. The vertical forces acting is(i) Force P1A acting vertically down on the top surface. (ii) Weight mg of the liquid column acting vertically downwards. (iii) Force P2A at the bottom surface acting vertically upwards, where P1 and P2 are the pressures at the top and bottom faces. A is the area of the cross-section of the circular face and m is the mass of the cylindrical liquid column. 29.Diffrentiate between steady and unsteady flow.(Nov/Dec 2017) A flow that is not a function of time is called steady flow. Steady-state flow refers to the condition where the fluid properties at a point in the system do not change over time. A flow that is a function of time is called Unsteady flow. UnSteady flow refers to the condition where the fluid properties at a point in the system will change over time. PART – B 1. The space between two square flat parallel plates is filled with oil. Each side of the plate is 60 cm. The thickness of the oil film is 12.5 mm. The upper plate, which moves at 2.5 m/s requires a force of 98.1 N to maintain the speed. Determine the dynamic viscosity of the oil and the kinematic viscosity of the oil in stokes if the specific gravity of the oil is 0.95. 2. A 400 mm diameter shaft is rotating at 200 r.p.m. in a bearing of length 120 mm. If the thickness of oil film is 1.5 mm and the dynamic viscosity of the oil is 0.7 N.s/m 2 determine: (i) Torque required to overcome friction in bearing (ii) Power utilised in overcoming viscous resistance. (Nov/Dec 2016) 3. A vertical cylinder of diameter 180 mm rotates concentrically inside another cylinder of diameter 181.2 mm. Both the cylinders are 300 mm high. The space between the cylinders is filled with a liquid. Determine the viscosity of the fluid if a torque of 20 Nm is required to rotate the inner cylinder at 120 r.p.m. 4. Find the surface tension in a soap bubble of 40 mm diameter when the inside pressure is 2.5 N/m2 above atmospheric pressure. 5. Calculate the capillary rise in a glass tube of 4 mm diameter, when immersed in (i)water, and (ii)mercury.the temperature of the liquid is 20oC and the values of the surface tension of water and mercury at 20oC in contact with air are 0.073575 N/m respectively. The angle of contact for water is zero that for mercury 130o. Take density of water at 20oC as equal to 998 kg/m3.

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6. A pipe (1) 450 mm in diameter branches in to two pipes (2 and 3) of diameters 300 mm and 200 mm respectively. If the average velocity in 450 mm diameter pipe is 3m/s. Find (i) Discharge through 450 mm diameter pipe; (ii) Velocity in 200 mm diameter pipe if the average velocity in 300mm pipe is 2.5 m/s. 7. A 6m long pipe is inclined at an angle of 20 o with the horizontal. The smaller section of the pipe which is at lower level is of 100 mm dia and the larger section is of 300 mm dia. If the pipe is uniformly tapering and the velocity of the water at the smaller section is 1.8m/s. Determine the difference of pressures between two sections. 8. A 30 cm x 15 cm venturimeter is provided in a vertical pipe line carrying oil of specific gravity 0.9, the flow being upwards. The difference in elevation of the throat section and entrance section of the venturimeter is 30 cm. The differential U tube mercury manometer shows a gauge deflection of 25 cm. Calculate: (i) the discharge of oil. (ii) The pressure difference between the entrance section and the throat section. Take Cd=0.98 and specific gravity of mercury as 13.6. 9. A horizontal venturimeter with inlet and throat diameter 300 mm and 100 mm respectively is used to measure the flow of water. The pressure intensity at inlet is 130 kN/m 2 while the vacuum pressure head at throat is 350 mm of mercury. Assuming that 3% head lost between the inlet and throat. Find the value of coefficient of discharge for the venturimeter and also determine the rate of flow. 10. An orifice meter with orifice diameter 15 cm is inserted in a pipe of 30 cm diameter. The pressure difference measured by a mercury oil differential manometer on the two sides of the orifice meter gives a reading of 50 cm of mercury. Find the rate of flow of oil of sp.gr 0.9 and Cd = 0.6. 11. Derive Euler’s equation of motion. 12. Determine the viscous drag torque and power absorbed on one surface of collar bearing of 0.2m ID and 0.3 m OD with a oil film thickness of 1mm and viscosity of 30 centi-poise if it rotates at 500 rpm (Nov/Dec 2015) 13. The water level in the tank is 20m above the ground. The hose is connected to the bottom of tank, and the nozzle is at the end of hose is pointed straight up. The tank is at sea level and the water surface is open to atmosphere. In the line leading from the tank to the nozzle is a pump, which increases the pressure of water. If the water jet rises to the height of 27m from the ground, determine the minimum pressure rise applied by the pump to the water line. (Apr/May 2015) 14. A hollow cylinder of 150mm OD with its weight equal to the buyont forces is to be kept floating vertically in the liquid with a surface tension of 0.45N/m 2. The contact angle is 60º. Determine the additional force required. (Apr/May 2015) 15. At a certain location, wind at a temperature of 30 °C is blowing steadily at 15 m/s .Determine the mechanical energy of air per unit mass and the power generation potential of a wind turbine with 40 m diameter blades at that location. Also determine the actual electric power generation assuming an overall efficiency of 35%. (May/June 2016) St.Joseph’s College of Engineering

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Mechanical Engineering

16. In cold climates the water pipes may freeze and burst if proper precautions are not taken. In such an occurrence, the exposed part of a pipe on the ground ruptures, and water shoots up to 34 m. Estimate the gage pressure of water in pipe. State your assumptions and discuss if the actual pressure is more or less than the value you predicted. (May/June 2016) 17. Derive Reynolds transport theorem (Nov/Dec 2016) 18. Derive Bernoullis equation with basic assumptions (Nov/Dec 2016 &Apr/May 2017) 19. (a) Calculate the dynamic viscosity of an oil which is used for lubrication between a square plate of size 0.8m x 0.8 m in an inclined plane with an angle of inclination 30° to the horizontal. The weight of the square plate is 300 N and it slides down the inclained plane with an uniform velocity of 0.3m/s. The thickness of the oil flim is 1.5mm (b)An oil of sp.gravity 0.8 is flowing through venturimeter having inlet dia 20cm and throt dia 10cm. The oil – mercury differential manometer shows a reading of 25cm. Calculate the discharge of oil through the horizontal venturimeter. Take Cd = 0.98 (Apr/May 2017) 20.A U tube manometer is used to measure water in a pipe line which is in excess of atmospheric pressure. The right limb of the manometer contains mercury and is open to atmosphere/ The contact between the water and mercury is in the left limb.Calculate the pressure of water in the mainline if the difference in level of mercury in the limbs is 10.5 cm and free surface of mercury is in level with centre of pipe.If the pressure of water in the pipe is reduced by (i) 10000N/m 2 and (ii) 12000 N/m2. Find the new difference if level of mercury. (Nov/Dec 2017) PART -C 1. A conical bearing of Outer radius 0.5 m and inner radius 0.3 m runs on a conical support with a uniform clearance between surfaces. Oil with viscocity 33 centi poise is used. The support is rotated at 450 rpm. Determine the clearance if power required was 1400 W. (May/June 2016) 2. A hydraulic lift shaft of 450 mm diameter moves in a cylinder of 451 mm diameter with the length of engagement of 3m. The interface is filled with oil of kinematic viscocity of 2.5 x 10 -4 m2/s and the density of 900 kg/m3. Determine the uniform velocity of movement of the shaft if the drag resistance was 320 N. (May/ June 2016) 3. Water flows at a rate of 200 lit/s upwards through a tapered vertical pipe . The diameter of bottom is 240 mm and the top is 200 mm length is 5m , the pressure at the bottom is 8 bar and pressure at the top is 7.3 bar. Determine the head loss through the pipe. Express as the function of exit velocity head. (Nov/Dec 2015) 4. In a vertical pipe carring water, pressure gauges inserted at points x and y where the pipe diameters are 0.2m and 0.1m respectively. The point y is 2.25m below x and when the flowrate down the pipe is 0.025m3/s, the pressure at y is 15686 N/m 2 greater than that at x. Assuming the losses in the pipe between x and y can be expressed as (k . v 2/2g) where v is velocity at x find the value of k. If the gauge at x and y are replaced by tubes with water and connected to U-Tube containing mercury of relative density 13.6 Calculate the difference in the levels of two limbs of the U-tube. (Nov/Dec 2017) St.Joseph’s College of Engineering

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Mechanical Engineering

UNIT II FLOW THROUG CIRCULAR CONDUITS PART – A 1. Mention the general characteristics of laminar flow. •

There is a shear stress between fluid layers

•

‘No slip’ at the boundary

•

The flow is rotational

•

There is a continuous dissipation of energy due to viscous shear

2. What is Hagen poiseuille’s formula?(Nov/Dec 2012) P1-P2 / g = h f = 32 µUL / 2gD The expression is known as Hagen poiseuille formula. Where P1-P2 / g = Loss of pressure head

U = Average velocity

µ = Coefficient of viscosity

D = Diameter of pipe

L = Length of pipe 3. What are the factors influencing the frictional loss in pipe flow? Frictional resistance for the turbulent flow is i. Proportional to vn where v varies from 1.5 to 2.0. ii. Proportional to the density of fluid. iii. Proportional to the area of surface in contact. iv. Independent of pressure. v. Depend on the nature of the surface in contact. 4. What is the expression for head loss due to friction in Darcy formula? hf = 4fLV2 / 2gD Where,

f = Coefficient of friction in pipe; D = Diameter of pipe;

L = Length of the pipe; V = velocity of the fluid

5. What do you understand by the terms a) major energy losses, b) minor energy losses Major energy losses: This loss due to friction and it is calculated by Darcy weisbach formula and chezy’s formula. Minor energy losses:This is due to, i. Sudden expansion in pipe. ii. Sudden contraction in pipe. iii. Bend in pipe. iv. Due to obstruction in pipe . 6. Give an expression for loss of head due to sudden enlargement of the pipe: he = (V1-V2)2 /2g Where he = Loss of head due to sudden enlargement of pipe . V1 = Velocity of flow at section 1-1, V2 = Velocity of flow at section 2-2 7. Give an expression for loss of head due to sudden contraction: (Apr/May 2015) hc =0.5 V2/2g here, c = Loss of head due to sudden contraction; St.Joseph’s College of Engineering

V = Velocity at outlet of pipe. 11

CE8394 - Fluid Mechanics and Machinery 2018-2019

Mechanical Engineering

8. Give an expression for loss of head at the entrance of the pipe: hi =0.5V2/2g Where, hi = Loss of head at entrance of pipe;

V = Velocity of liquid at inlet and outlet of the pipe.

9. Define the terms a) Hydraulic gradient line [HGL], b) Total Energy line [TEL] (Nov/Dec 2015) a) Hydraulic gradient line: Hydraulic gradient line is defined as the line which gives the sum of pressure head and datum head of a flowing fluid in apipe with respect the reference line. b) Total energy line: Total energy line is defined as the line which gives the sum of pressure head, datum head and kinetic head of a flowing fluid in a pipe with respect to some reference line. 10. What is sypon ? Where it is used? Sypon is along bend pipe which is used to transfer liquid from a reservoir at a higher elevation to another reservoir at a lower level. Uses of sypon : 1. To carry water from one reservoir to another reservoir separated by a hill ridge. 2. To empty a channel not provided with any outlet sluice. 11. What are the basic educations to solve the problems in flow through branched pipes? i. Continuity equation. ii. Bernoulli’s formula; iii. Darcy weisbach equation. 12. What is Dupuit’s equation or equivalent pipe equation?(Nov/Dec 2013&Apr/May 2017) L1/d15+L2/d25 +L3/d35 = L / d5 Where L1, d1 = Length and diameter of the pipe 1, L2, d2 = Length and diameter of the pipe 2 L3, d3 = Length and diameter of the pipe 3 13. Define kinetic energy correction factor? Kinetic energy factor is defined as the ratio of

the

kinetic energy of the flow per sec based on

actual velocity across a section to the kinetic energy of the flow per sec based on average velocity across the same section. It is denoted by (α). 14. What is Hydraulic mean depth? It is the ratio of Cross-sectional area of the flow and Wetted perimeter, where wetted perimeter is the perimeter of the pipe or the channel which remains in contact with the flowing fluid. 15. What do you understand by the transmission efficiency of a pipe? μ = Power available at the end of the pie/ Power available at the entry of the pipe. 16. Obtain a condition for maximum efficiency and prove that it is 66.7%? hf 

H 3

The maximum η is given by (H-(H/3))/H = 66.7%

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17. Differentiate Laminar & Turbulent Flow : Laminar Flow 1) A flow is said to be laminar if Renolds

1)

A

Turbulent Flow flow is said to be turbulent if

number is less than 2000 is known as Renolds number is greater than

4000

is

Laminar flow. known as Turbulent flow . 2) Laminar flow is possible only at low 2) Is the flow is possible at both velocities and high viscous fluids . velocities and low viscous fluid. 3) In such type of flow fluid particle 3) In that typeof flow fluid particle moves

in laminas

or layers

gliding move in a zig – zag manner .

smoothly over the adjacent layer. 18. What do you meant by viscous flow? A flow is said to be viscous if the Renold’s number is less than 2000 (or) the flows in layers ie. Re<2000. 19. State the Relationship between Shear stress and pressure gradient. The Relationship between Shear stress and pressure gradient,

,indicates that the pressure

gradient in the direction of flow is equal to the shear gradient in the direction normal to the direction of flow. 20. What is an equivalent pipe? State the assumptions made in finding the equivalent length of a compound pipe. (Apr/May 2015 & Apr/May 2017) A compound pipe consisting of several pipes of varying diameters and length may be replaced by a pipe of uniform diameter is known as equivalent pipe. a) The material of the pipe is same, and hence the co efficient is same b) The minor losses are neglected. 21. Brief on Darcy’s weibach’s equation. (May/June 2016) The Darcy–Weisbach equation is a phenomenological equation, which relates the head loss, or pressure loss, due to friction along a given length of pipe to the average velocity of the fluid flow for an incompressible fluid. 22. What is the condition for maximum power transimission w.r.t head available ? (May/June 2016) The condition for maximum power transimission is head loss due to friction is one third of total head available,

H = 3hf

23. Find the displacement thickness for the velocity distribution is given by (Nov/Dec 2016)

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The displacement thickness for the velocity distribution is δ*= 24.Draw the velocity distribution and shear stress distribution for the flow through circular pipes. (Nov/Dec 2016)

25.Define boundary layer. (Apr/May 2017) The layer adjacent to the boundary is known as boundary layer. It is formed whenever there is a relative motion between the boundary and the fluid. 26. State significance of Navier – stokes equation. (Nov/Dec 2017) The Navier-Stokes equations, developed by Claude-Louis Navier and George Gabriel Stokes in 1822, are equations which can be used to determine the velocity vector field that applies to a fluid, given some initial conditions. They arise from the application of Newton’s second law in combination with a fluid stress (due to viscosity) and a pressure term which is used to solve real situations. 27. What is meant by roughness Reynolds number. (Nov/Dec 2017) The Reynolds number depends upon the surface in which the fluid flows so the surface roughness is related to frictional resistance. The friction factor becomes constant at high Reynolds number and it is called as Roughness Reynolds number PART - B 1. Derive an expression for Darcy–Weisbach formula to determine the head loss due to friction.

Give the expression for relation between friction factor ‘f’and Reynolds's number ‘Re’for laminar and turbulent flow. 2. A 30 cm diameter pipe of length 30 cm is connected in series to a 20 cm diameter pipe of length

20 cm to convey discharge. Find the equivalent length of pipe of diameter 25 cm, assuming that the Friction factor remains the same and the minor losses are negligible. (Nov/Dec 2012) 3. An oil of viscosity 9 poise and specific gravity 0.9 is flowing through a horizontal pipe of 60 mm

diameter. If the pressure drop in 100 m length of the pipe is 1800 kN/m 2, determine . i. The rate of flow of oil. ii. The centre-line velocity, iii. The total frictional drag over 100 m length, iv. The power St.Joseph’s College of Engineering

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required to maintain the flow, v. The velocity gradient at the pipe wall, vi.The velocity and shear stress at 8 mm from the wall. 4. The velocity distribution in the boundary layer is given by

, being boundary

layer thickness. Calculate the following: i.Displacement thickness, ii. Momentum thickness, and iii. Energy thickness. 5. The rate of flow of water through a horizontal pipe is 0.25 m 3/sec. The diameter of the pipe is

suddenly enlarged from 200 mm to 400 mm. The pressure intensity in the smaller pipe is 11.772 N/cm2. Determine (i) loss of head due to sudden enlargement (ii) pressure intensity in the large pipe and (iii) power lost due to enlargement. 6. Three pipes of diameters 300 mm, 200 mm and 400 mm and lengths 450 m, 255 m and 315 m

respectively are connected in series. The difference in water surface levels in two tanks is 18 m. Determine the rate of flow of water if coefficients of friction are 0.0075, 0.0078 and 0.0072 respectively considering. 7. A piping system consists of three pipes arranged in series; the lengths of the pipes are 1200 m,

750 m, and 600 m and diameters 750 mm, 600 mm and 450 mm respectively. (1) Transform

the

system to an equivalent 450 mm diameter pipe and (2) Determine an equivalent diameter for the pipe 2550 m long. 8. For sudden expansion in a pipe flow, workout the optimum ratio between the diameter of the

pipe before expansion and the diameter of the pipe after expansion, so that the pressure rise is maximum. 9. Water is supplied to the inhabitants of a college campus through a supply main. The following

data is given: Distance of the reservoir from the campus = 3000 m, number of inhabitants = 4000, Consumption of water per day of each inhabitant = 180 litres. Loss of head due to friction = 18m, Co efficient of friction for the pipe, f=0.007; If half of the daily supply is to be pumped in 8 hrs, Find the size of the supply main. 10. The rate of flow of water through a horizontal pipe is 0.25 m 3/s. The diameter of the pipe which is 20

cm is suddenly enlarged to 40 cm. The pressure intensity in the smaller pipe is 11.772 N/cm 2. Determine the loss of head due to sudden enlargement and pressure intensity in the large pipe. 11. Two reservoirs whose water surface elevations differ by 12 m are connected by the following

horizontal compound pipe system starting from the high level reservoir. Take L1 = 200 m, D1 = 0.2 m, f1  0.008 and L 2 = 500 m, D 2 = 0.3 m, f 2 = 0.006. Considering all head losses and assuming that all

changes of section are abrupt, compute the discharge through the system. Find the equivalent length of a 0.25 m diameter pipe if minor losses are neglected and friction factors are assumed to be the same. Sketch HGL and TEL. 12. Describe moody’s chart. (Apr/May 2015) St.Joseph’s College of Engineering

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13. Oil at 27º C (ρ=900 kg/m 3 and µ = 40 centi-poise) is flowing steadily in a 1.25 cm diameter,

40m long. During the flow, the pressure at inlet and exit of pipe is 8.25 bar and 0.97 bar. Determine the flow rate of oil through the pipe if pipe is (a) horizontal (b) inclined 20º upward (c) inclined 20º downward (Apr/May 2015) 14. A shell and tube heat exchanger with hundreds of tubes housed in a shell are commonly used in

practice for a heat exchange between two fluids. Such a heat exchanger is used in a active solar hot water system transfers heat from a water antifreeze solution flowing through shell and the solar collector to fresh water flowing through the tubes at an average temperature of 60°C at a rate of 15 L/s. The heat exchanger contains 80 brass tubes 1 cm in inner diameter and 1.5 m in length. Disregarding inlet, exit and header losses, determine the pressure drop across a single tube and the pumping power required by the tubeside fluid of the heat exchanger. The density and dynamic

viscosity of water at 60°C are

= 983.3 kg/m3 and µ= 0.467 x 10-3 kg/ms, respectively. The

roughness of brassing tube is 1.5 x 10-6 m. (May/June 2016) 15. Derive the Hagen poiseuille’s formula for the flow through circular pipes?(Nov/Dec 2016) 16. (a) A fluid of viscosity 0.7Pa and Sp.gravity 1.3 is flowing through a pipe dia 120mm the Max

shear stress at the pipe is 205.2 N/m2 Determine the pressure gradient, Reynolds number and average velocity. (b) A crude oil of kinematic viscosity 0.4 Strokes is flowing through a pipe of dia 300mm at the rate of 300 lit/s Find the head loss due to friction for a length of 50m of the pipe. Take the Coefficient of friction as 0.06(Apr/May 2017) 17. For a flow of viscous fluid flowing through a circular pipe under laminar flow conditions show

that the velocity distribution is a parabola and also show that the average velocity is half of the max velocity. (Apr/May 2017) 18. Water flowing through a 10cm diameter pipe enters a porous section of same diameter which

allows a uniform radial velocity Vw through the wall surfaces for a distance of 2m (i) If the entrance average velocity V1 = 12m/s Find the exit velocity V2 If Vw = 15cm/s out of the pipe walls; Vw = 10cm/s into the pipe what value of Vw will make V2 = 9m/s (ii) If the entrance average velocity V1 is 18m/s find the exit velocity V2 If Vw= 18cm/s out of the pipe walls; Vw =12cm/s into the pipe. What value of Vw will make V2= 12m/s? (Nov/Dec 2017) PART -C 1.Two reservoirs are connected by a pipeline 600m long. For the first 300m, its diameter is 15cm that reduces suddenly to 7.5cm for the remaining portion. Water discharges into the side of the lower reservoir below the water surface. If the difference in the water level between the two reservoirs is 80m, estimate the discharge considering all losses. Assume C c= 0.867 and 4f = 0.0268. Determine the viscous St.Joseph’s College of Engineering

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drag torque and power absorbed on one surface of collar bearing of 0.2m ID and 0.3 m OD with a oil film thickness of 1mm and viscosity of 30 centi-poise if it rotates at 500 rpm (Nov/Dec 2015) 2. An oil of specific gravity 0.80 and kinematic viscosity 15 x 10 -6 m2/s, flow in a smooth pipe of 12cm

diameter at a rate of 150 litre/min. Determine whether the flow is laminar or turbulent. Also calculate the velocity at the center line and velocity at the radius of 4cm. What is the head loss for a length of 10m? what will be the entry length? Also determine the wall shear. (Nov/Dec 2015) 3. Three pipes of diameters 400 mm, 200 mm and 300 mm and lengths 400 m, 300 m and 200 m

respectively are connected in series. The difference in water surface levels in two tanks is 16m. If the coefficients of friction of all the pipes are same and equal to 0.005, determine the discharge through the compound pipe neglecting first the minor losses and then including them. (Nov/Dec 2016) 4. Water at 15°C is to be discharged from reservoir at a rate of 20L/s using two horizontal cast iron

pipes connected in series and a pump between them. The first pipe is 22 m long and has a 6 cm diameter, while the second pipe is 33 m long and has a 4 cm diameter. The water level in the reservoir is 30 m above the centerline of the pipe. The pipe entrance is sharp-edged, losses associated with the connection of pump is negligible. Determine the required pumping head and the minimum pumping power to maintain the indicated flow rate. The density and dynamic viscocity of water at 15°C are ρ= 999.1 kg/m3 and µ= 1.138 x 10-3kg/ms. The roughness of cast iron pipe is 0.00026 m. (May/June 2016 & Nov/Dec 2017) UNIT III DIMENSIONAL ANALYSIS PART – A 1. What are the types of fluid flow? Steady & unsteady fluid flow,Uniform & Non-uniform flow, One dimensional, two-dimensional & three-dimensional flows, Rotational &Irrotational flow 2. Name the different forces present in fluid flow Inertia force;viscous force; Surface tension force; Gravity force. 3. When in a fluid considered steady? In steady flow, various characteristics of following fluids such as velocity, pressure, density, temperature etc at a point do not change with time. So it is called steady flow. 4. Give the Euler’s equation of motion?(Nov/Dec 2012) (dp/p)+gdz+vdv=0 5. What are the assumptions made in deriving Bernouillie’s equation? (Nov/Dec 2015) 1.The fluid is ideal; 2.The flow is steady; 3.The flow is incompressible; 4.The flow is irrotational. 6. What is bernouillie’s equation for real fluid? (p1/g)+(v12/2g)+z1=(p2/g)+(v22/2g)+z2+hl wherehl is the loss of energy (p/g)-Pressure energy. (v2/2g)=Kinetic energy. St.Joseph’s College of Engineering

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z-Datum energy. 7. State the application of Bernouillie’s equation? It has the application on the following devices.1.Orifice meter; 2.Venturimeter.; 3.Pitot tube. 8. State the methods of dimensional analysis. 1. Rayleigh’s method; 2. Buckingham’s Π theorem

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9. State Buckingham’s Π theorem. (Nov/Dec 2012, Nov/Dec 2016) It states that if there are ‘n’ variables in a dimensionally homogeneous equation and if these variables contain ‘m’ fundamental dimensions (M,L,T), then they are grouped into (n-m), dimensionless independent Π-terms. 10. State the limitations of dimensional analysis. 1. Dimensional analysis does not give any due regarding the selection of variables. 2.The complete information is not provided by dimensional analysis. 3.The values of coefficient and the nature of function can be obtained only by experiments or from mathematical analysis. 11. Define Similitude Similitude is defined as the complete similarity

between the model and prototype.

12. State Froude’s model law Only Gravitational force is more predominant force. The law states ‘The Froude’s number is same for both model and prototype’. 13. What are the factors influencing the frictional lossin pipe flow? Frictional resistance for the turbulent flow is, 1. Proportional to vn where v varies from 1.5 to 2.0, 2. Proportional to the density of fluid. 1. Proportional to the area of surface in contact, 4. Independent of pressure, 5. Depend on the nature of the surface in contact. 14. What are the factors to the determined when viscous fluid flows through the circularpipe? Velocity distribution across the section; Ratio of maximum velocity to the average velocity; Shearstress distribution; Drop of pressure for a given length. 15. What are the advantages of dimensional and model analysis? (Apr/May 2015) a. The performance of hydraulic structure or hydraulic machine can be easily predicted, in advance, from its model. b. The merits of alternative designs can be predicted with the help of model testing. The most economical and safe design may be, finally adopted. 16. Define mach number and state it’s application. (Nov/Dec 2015) Mach’s number is defined as the square root of the ratio of the inertia force of a flowing fluid to the elastic force. It is used in Aerodynamic testing ,Under water testing of torpedoes,Water – hammer problems 17. Write the similitude that exist between model and prototype (Apr/May 2017) Similitude is defined as the similarity between the model and its prototype in every respect. There are three types of similarities exists between the model and prototype, Geometric Similarity, Kinematic Similarity, Dynamic Similarity

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18. Define Froude's number. Froude’s number is defined as the square root of the ratio of inertia force of a slowing fluid to the gravity force. 19. What is Mach number? Mention its field of use. Mach’s number is defined as the square root of the ratio of the inertia force of a flowing fluid to the elastic force. It is used in Aerodynamic testing, Under water testing of torpedoes,Water – hammer problems 20. Distinguish between a control and differential control volume. The region in which the mass crosses the system boundary is called control volume. A control volume is a mathematical abstraction employed in the process of creating mathematical models of physical processes. The control volume in which the conservation of mass equation is applied is called a differential control volume. 21. Brief on Euler number. (May/June 2016) The Euler number (Eu) is a dimensionless number used in fluid flow calculations. It expresses the relationship between a local pressure drop caused by a restriction and the kinetic energy per volume of the flow, and is used to characterize energy losses in the flow, where a perfect frictionless flow corresponds to an Euler number of 0. The inverse of the Euler number is referred to as the Ruark Number with the symbol Ru. 22. What is meant by Kinematic Similarity ? (May/June 2016) Kinematic similarity is the similarity of time as well as geometry. It exists between model and prototype. If the paths of moving particles are geometrically similar. If the rations of the velocities of particles are similar. 23. write the scale ratio for velocity, pressure intensity using Froude model law. (Nov/Dec 2016) (i) Scale ratio for velocity vr = (ii) Scale ratio for pressure intensity pr = Lr 24.Write the expression for Mach number and state its application.(Apr/May 2017)

Applications (i)

Flow of aeroplane of supersonic speed

(ii)

Underwater testing of torpedoes.

(iii) Aerodynamic testing (iv)

Flow of missiles, rockets.

(v) Water hammer problem. 25. A piping system involves two pipes of different diameters (but of identical length, material and roughness) connected in parallel. How would you compare the flowrates and pressure drops in these two pipes. (Nov/Dec 2017)

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26. The excess pressure Δp inside a bubble is known to be a function of the surface tension and radius. By dimensional reasoning determine how the excess pressure will vary if we double the surface tension and radius. (Nov/Dec 2017) There is no change in pressure. Since, the surface tension as well as diameter doubles it does not affect the ratio.

PART - B 1. The resistance R experienced by a partially submerged body depends upon the velocity V, length of the body l, viscosity of the fluid µ, density of the fluid  and gravitational acceleration g, obtain a dimensionless expression for R. 2. Using Buckingham’s π theorem, show that the velocity through a circular orifice is given by

. Where H=Head causing flow, D=Diameter of the orifice, µ=Co-efficient of viscosity, =Mass density & g=Acc. due gravity. (Apr/May 2017) 3. The discharge Q of a centrifugal pump depends upon the mass density of fluid (), the speed of the pump (N), the diameter of the impeller (D), the manometric head (H m) and the viscosity of fluid

(µ).Show that

.

4. A pipe of diameter 1.m is required to transport an oil specific gravity 0.9 and viscosity 3 x 10 -2 poise at the rate of 3000 liters/s. Tests were conducted on a 15 cm diameter pipe using water at 20oC. Find the velocity and the rate of flow in the model. Viscosity of water at 20oC is 0.01 poise. 5. A model of submarine is scaled down to 1/20 of the prototype and is to be tested in a wind tunnel where free stream pressure is 2 MPa and absolute temperature is 50 oC. The speed of the prototype is 7.72 m/s. Determine the free stream velocity of air and the ratio of the drags between model and prototype. Assume kinematic viscosity of sea water as 1.4 x 10 -6 m2/s and viscosity of air as 0.0184 cP. 6. A ship model of scale 1/50 is towed through sea water at a speed of 1 m/s. A force of 2 N is required to tow the model. Determine the speed of the ship and the propulsive force on the ship, if prototype is subjected to wave resistance only.

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7. In an airplane model size 1/10 of its prototype the pressure drop is 7.5 kN/m 2. The model is tested in water. Find the corresponding pressure drop in the prototype. Take density of air is 1.24 kg/m3, density of water is 1000 kg/m3, Viscosity of air is 0.00018 poise and viscosity of water is 0.01 poise. (Nov/Dec 2016) 8. Using Buckingham’s π theorem, show that the drag FD of a supersonic aircraft is given by: FD  L2 V 2  (Re, M) . Where, Re  VL  = Reynolds number, M  V c = Mach number,

 = fluid density, c = sonic velocity =

K ,

V = velocity of aircraft, K = bulk modulus of fluid,

L = chord length, L2 = wing area = chord x span, ρ = a functional notation. 9. The resisting force (R) of a supersonic flight can be considered as dependent upon the length of the air craft 'ℓ', velocity 'v', air viscosity 'μ', air density 'ρ' and bulk modulus of air is 'k'. Express the functional relationship between these variables and the resisting force. 10. Check the following equations are dimensionally homogeneous (i) Drag force = Cd (ii) F=

1  U2 A 2

 Q (U1 - U 2 )  ( P1A 1 - P2 A 2 ) g

(iii) Total energy per unit mass = V2/2 + gz + p/ρ 11. Consider force F acting on the propeller of an aircraft, which depends upon the variable U,  , , D and N. Derive the non–dimensional functional form





F U2D 2  f ((UD /  ),(N D / U)).

12. An object of diameter 900 mm is to move in air at 60 m/s. Its drag is to be estimated from tests on a half scale model in water. The drag on the model is 1140 N. Estimate the speed of the model and drag on the full scale object. Given,  air = 1.2 kg/m3,  air = 1.86  10–5 Ns/m2,  water = 1.0110–3 Ns/m2,  water = 1000 kg/m3 13. A model of a hydro electric power station tail race is proposed to built by selecting vertical scale 1 in 50 and horizontal scale 1 in 100. If the design pipe has flow rate of 600 m 3/s and the allowable discharge of 800 m3/s. Calculate the corresponding flow rates for the model testing. (Nov/Dec 2015) 14. The power developed by hydraulic machines is found to depend on head H, flow rate Q, density ρ, speed N, runner diameter D, and acceleration due to gravity G. obtain suitable dimensionless parameters to correlate experimental results. (Apr/May 2015) 15. Obtain a relation using dimensional analysis for the resistance to uniform motion of a partial submerged body in a viscous compressible fluid. (Apr/May 2015) 16. The temperature difference θ at location x at time τ in a slab of thickness L originally at a temperature difference θₒ with outside is found to depend on the thermal diffusivity α, thermal conductivity k and convection coefficient h. using dimensional analysis, determine dimensionless parameter that will correlate the phenomenon. (May/June 2016) 17. Convective heat transfer coefficient in free convection over a surface is found to be influenced by the density, viscosity, thermal conductivity, coefficient of cubical expansion, temperature St.Joseph’s College of Engineering

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difference, gravitational acceleration, specific heat, the height of surface and flow velocity. Using dimensional analysis, determine the dimensionless parameters that will correlate the phenomenon. (May/June 2016) 18. Define similitude and its types. (Nov/Dec 2016) 19. Derive the five diffrent types of dimension less number. (Nov/Dec 2016) 20. Vortex shedding at the rear of the structure of a given section can create harmfull periodic vibration. To predict the shedding frequency a smaller model is to be tested in a water tunnel. The air speed is expected to be 90kmph. If the geometric scale is 1:6.8 and the water temperature is 28oC determine the speed to be used in the tunnel Consider the air temperature as 40 oC If the shedding frequency of model was 60 Hz determine the shedding frequency of proptotype, the dimensions of the structure are dia 0.2m and height 0.4m (Nov/Dec 2017) 21. Consider flow over a very small object in a viscous fluid. Analysis of the equation of motion shows that the inertial terms are much smaller than the viscous and pressure terms. It turns out, the the fluid density drops out of the equation of the motion. The only important parameter of the problem are velocity of motion U, Viscosity of the fluid µ and length scale of the body, using the Buckingham pi theorem generate an expression for two dimensional drag D2-D as a function of other parameter of the problem. Use cylinder diameter d as the appropriate length scale. Repeat the dimensional analysis with ρ included as a parameter. Find the non-dimensional

relationship

between parameters in the problem. (Nov/Dec 2017) PART – C 1.

Model of an air duct operating with water produces a pressure drop of 10 kN/m 2 over 10 m

length. If the scale ratio is 1/50. Density of water is 1000 kg/m 3 and density of air is 1.2 kg/m3. Viscosity of water is 0.001 Ns/m2 and viscosity of air is 0.00002 Ns/m2. Estimate corresponding drop in a 20 m long air duct. (Nov/Dec 2015) 2. It is desired to obtain the dynamic similarity between a 30 cm diameter pipe carrying linseed oil at 0.5 m3/s and a 5 m diameter pipe carrying water. What should be the rate of flow of water in lps? If the pressure loss in the model is 196 N/m 2, what is the pressure loss in the prototype pipe? Kinematic viscosities of linseed oil and water are 0.457 and 0.0113 stokes respectively. Specific gravity of linseed oil = 0.82. 3. A 1:100 model is used for model testing of ship. The model is tested in wind tunnel the length of the ship is 400m the velocity of the wind tunnel around the model is 25 m/s and the resistence is 55 N Determine the length of the model. Also find the velocity of the ship as well as resistance developed. Take density of air and sea water as 1.24 kg/m3 and 1030 kg/m3. The kinematic viscosity of air and sea water are 0.018 stokes and 0.012 stokes respectively (Apr/May 2017) 4. The pressure difference P in a pipe of diameter D and length l due to turbulent flow depends on the velocity V, viscosity μ, density ρ and roughness K. By using dimensional analysis, obtain an expression for the pressure difference P .(Nov/Dec 2016) UNIT IV PUMPS St.Joseph’s College of Engineering

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PART – A 1. What is meant by Pump? It is defined as the hydraulic machine in which converts the mechanical energy into hydraulic energy, which is mainly in the form of pressure energy. 2. What is Euler equation of motion? How will you obtain Bernoulli’s equation from it? This is the equation of motion in which the forces due to gravity and pressure are taken in to consideration. Bernoulli’s equation is obtained by integrating the Euler’s equation of motion. 3. Mention main components of Centrifugal pump.(Nov/Dec 2012) Casing; Impeller; Suction pipe, strainer & Foot valve; Delivery pipe & Delivery valve 4. What is the slip in reciprocating pump? Slip is the difference between the theoretical discharge and actual discharge of the pump. Slip= Qth-Qact. 5. What is meant by Priming? (Nov/Dec 2016) 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. This is called as priming. 6. What are the main parts of reciprocating pump?(Nov/Dec 2012) A cylinder with a piston, Piston rod, connecting rod and a crank, Suction pipe, Delivery pipe. Suction valve and Delivery valve. 7. How will you classify the reciprocating pump? The reciprocating pump may be classified as, 1. According to the water in contact with one side or both sides of the piston. 2. According to the number of cylinders provided. Classification according to the contact of water is (1) Single acting (2) Double acting. According to the number of cylinders provided they are classified as, 1. Single Cylinder pump.2. Double cylinder pump, 3. Triple cylinder pump. 8. Define Mechanical efficiency. It is defined as the ratio of the power actually delivered by the impeller to the power supplied to the shaft. 9. Define overall efficiency. It is the ratio of power output of the pump to the power input to the pump.

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10. Define speed ratio, flow ratio. Speed ratio:

It is the ratio of peripheral speed at outlet to the theoretical velocity of jet

corresponding to manometric head. Flow ratio:

It is the ratio of the velocity of flow at exit to the theoretical velocity of jet

corresponding to manometric head. 11. Mention main components of Reciprocating pump. Piton or Plunger; Suction and delivery pipe; Crank and Connecting rod 12. Define Slip of reciprocating pump. When the negative slip does occur? The difference between the theoretical discharge and actual discharge is called slip of the pump. But in sometimes actual discharge may be higher then theoretical discharge, in such a case coefficient of discharge is greater then unity and the slip will be negative called as negative slip. 13. Why negative slip occurs in reciprocating pump? (May/June 2016) If actual discharge is more than the theoretical discharge the slip of the pump will be negative. Negative slip occurs only when delivery pipe is short, Suction pipe is long and pump is running at high speed. 14. What is indicator diagram? Indicator diagram is nothing but a graph plotted between the pressure head in the cylinder and the distance traveled by the piston from inner dead center for one complete revolution of the crank. 15. What is meant by Cavitation? What will be its effects?( Apr/May 2017) It is defined phenomenon of formation of vapor bubbles of a flowing liquid in a region where the pressure of the liquid falls below its vapor pressure and the sudden collapsing of these vapor bubbles in a region of high pressure.The Effects of Cavitation will damage the pipe walls and also corrodes the pipes. 16. What are rotary pumps? Rotary pumps resemble like a centrifugal pumps in appearance. But the working method differs. Uniform discharge and positive displacement can be obtained by using these rotary pumps; It has the combined advantages of both centrifugal and reciprocating pumps. 17. What is an air vessel? (Nov/Dec 2016) An air vessel is a closed chamber containing compressed air in the top portion and liquid at the bottom of the chamber. At the base of the chamber there is an opening through which the liquid may flow into the vessel or out of the vessel. 18. What is the purpose of an air vessel fitted in the pump?( Apr/May 2017) 1. To obtain a continuous supply of liquid at a uniform rate. 2. To save a considerable amount of work in overcoming the frictional resistance in the suction and delivery pipes, and 3. To run the pump at a high speed without separation. 19. What is the relation between Work done of a Pump and Area of Indicator Diagram? Work done by the pump is Proportional to the area of the Indicator diagram. St.Joseph’s College of Engineering

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20. What is the work saved by fitting a air vessel in a single acting, double acting pump? Work saved by fitting air vessels in a single acting pump is 84.87%, In a double acting pump the work saved is 39.2%. 21. Define coefficient of discharge of reciprocating pump? It is defined as the ratio of actual discharge to theoretical discharge of reciprocating pump. Cd=Qa/Qth. 22. List the losses in centrifugal pump. (Nov/Dec 2015) (i) Mechanical friction losses between the fixed and rotating parts in the bearings and gland and packing. (ii) Disc friction loss between the impeller surfaces and the fluid. (iii) Leakage and recirculation losses. The recirculation is along the clearance between the impeller and the casing due to the pressure difference between the hub and tip of the impeller. 23. What is meant by NPSH? (Nov/Dec 2015&Nov/Dec 2017) The Negative Positive Suction Head (NPSH) is defined as the absolute pressure head at the inlet to pump, minus the vapour pressure head (in absolute units) plus the velocity head. NPSH = Absolute pressure head at inlet of the pump – vapour pressure head (absolute units) + velocity head 24.Define manometric efficiency and Mechanical efficiency (Apr/May 2015) Manometric efficiency is the ratio of the manometric head to the head imparted by the impeller to the water �𝑚𝑎� = 𝑀𝑎�𝑜𝑚𝑒𝑡𝑟𝑖� ℎ𝑒𝑎� /ℎ𝑒𝑎� 𝑖𝑚𝑝𝑎𝑟𝑡𝑒� 𝑏� 𝑖𝑚𝑝𝑒𝑙𝑙𝑒𝑟 𝑡𝑜 𝑤𝑎𝑡𝑒r

Mechanical efficiency is the ratio of the power available at the impeller to the power at the shaft of the centrifugal pump �𝑚𝑒�ℎ = 𝑃𝑜𝑤𝑒𝑟 𝑎𝑡 𝑡ℎ𝑒 𝑖𝑚𝑝𝑒𝑙𝑙𝑒𝑟 / 𝑃𝑜𝑤𝑒𝑟 𝑎𝑡 𝑡ℎ𝑒 𝑠ℎ𝑎�t

25.What are the operating characteristic curves of centrifugal pump. (Apr/May 2015)

26.Why is forward curved blading rarely used in pumps ? (May/June 2016) Mostly pumps are used for fluids of incompressible regime such as water so they use backward curved blades, whereas for the fluids which are compressible such as air requires forward blading which is so rare using pumps.

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27.Draw the outlet velocity triangle for a forward curved centrifugal pump.(Nov/Dec 2017)

PART - B 1. Explain about working principle of centrifugal pump. 2. A centrifugal pump is to discharge 0.118m3/s at a speed of 1450 rpm against a head of 25m. The impeller diameter is 250mm. Its width at outlet is 50mm and the manometric efficiency is 75%. Find the vane angle at outer periphery of the impeller. 3. A centrifugal pump is to discharge 0.12 m 3/sec at a speed of 1450 rpm against a head of 25m. The impeller diameter is 250mm, its width at outlet is 50mm and manometric efficiency is 75 percent. Find the vane angle at the outer periphery of the impeller. 4. Two geometrically similar pumps are running at the same speed of 1000rpm. One pump has an impeller diameter of 0.30m and lifts water at the rate of 20 litres per second against a head of 15m. Determine the head and impeller diameter of the other pump to deliver half the discharge. 5. The diameter and width of a centrifugal pump impeller are 300 mm and 60 mm respectively. The pump is delivering 144 litres of liquid per second with a manometric efficiency of 85 per cent. The effective outlet vane angle is 30. If the speed of rotation is 950 rpm. Calculate the specific speed of the pump. 6. The centrifugal pump has the following characteristics. Outer diameter of impeller = 800 mm; width of the impeller vane at outlet = 100 mm. angle of the impeller vanes at outlet = 40º.The impeller runs at 550 rpm and delivers 0.98 m 3/s under an effective head of 35 m. A 500 kW motor is used to drive the pump. Find the manometric, mechanical and overall efficiencies of the pump. Assume water enters the impeller vanes radially at inlet. 7. The impeller of a centrifugal pump having external and internal diameters 500 mm and 250 mm respectively, width at outlet 50 mm and running at 1200 r.p.m. works against a head of 48 m. The velocity of flow through the impeller is constant and equal to 3.0 m/s. The vanes are set back at an angle of 40 at outlet. Find: (i) Inlet vane angle (i) Work done by the impeller on water per second (iii) Manometric efficiency. (Apr/May 2017) 8. Explain about working principle of Reciprocating pump. (Nov/Dec 2013) 9. Explain about rotary positive displacement pumps. (Nov/Dec 2013)

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10. The diameter and stroke length of a single acting reciprocating pump are 150mm and 300mm respectively, the pump runs at 50rpm and lifts 4.2 lps of water through a height of 25m. The delivery pipe is 22m long and 100mm in diameter. Find (i) Theoretical power required to run the pump (ii) % of slip and (iii) Acceleration head at the beginning and middle of the delivery stroke (Apr/May 2017) 11. The diameter and length of a suction pipe of a single acting reciprocating pump are 10Cm and 5m respectively. The pump has a plunger diameter of 15cm and a stroke length of 35cm. The center of the pump is 3m above the water surface in the sump. The atm. Pressure head is 10.3m of water and the pump runs at 50rpm. Find (i) pressure head due to Acceleration at the beginning of the suction stroke. (ii) maximum pressure head due to Acceleration and (iii) pressure head in the cylinder at the beginning and end of the suction stroke. 12. Show from first principles that work saved in a single acting reciprocating pump, by fitting an air vessel is 84.8 percent. 13. A double acting reciprocating pump running at 60 rpm is discharging 1.5 m 3 of water per minute. The pump has a stroke length of 400 mm. The diameter of the piston is 250 mm. The delivery and suction heads are 20m and 5m respectively. Find the power required to drive the pump and the slip of the pump. 14. What is Air vessel and write the expression for workdone by the reciprocating pump fitted with Air vessel. Closed chamber containing compressed air in the top portion 15. A single acting reciprocating pump has a bore of 200 mm and a stroke of 350 mm and runs at 45 rpm. The suction head is 8 m and the delivery head is 20 m. Determine the theoretical discharge of water and power required. If slip is 10%, what is the actual flow rate? 16. A double acting reciprocating pump has a bore of 150 mm and stroke of 250 mm and runs at 35 rpm. The piston rod diameter is 20 mm. The suction head is 6.5 m and the delivery head is 14.5 m. The discharge of water was 4.7 l/s. Determine the slip and the power required. 17. In a single acting reciprocating pump with plunger diameter of 120 mm and stroke of 180 mm running at 60 rpm, an air vessel is fixed at the same level as the pump at a distance of 3 m. The diameter of the delivery pipe is 90 mm and the length is 25 m. Friction factor is 0.02. Determine the reduction in accelerating head and the friction head due to the fitting of air vessel. 18. In a reciprocating pump delivering water the bore is 14 cm and the stroke is 21 cm. The suction lift is 4 m and delivery head is 12 m. The suction and delivery pipe are both 10 cm diameter, length of pipes are 9 m suction and 24 m delivery. Friction factor is 0.015. Determine the theoretical power required. Slip is 8 percent. The pump speed is 36 rpm 19. Explain about performance characteristics of centrifugal pumps. (Nov/Dec 2015) 20. Discuss the working of lobe and vane pumps. (Apr/May 2015)

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21. Discuss about air vessel used with reciprocating pump . Asingle acting reciprocating pump handles water. The bore and the stroke of the unit are 22 cm and 32 cm. The suction pipe diameter is 12 cm and the length is 10 m. The delivery pipe is 12 cm and the length is 30 m. Take frictional factor 0.02. The speed of operation is 32 rpm. Determine the frictional power with and without air vessel. (May/June 2016) 22. Derive the expression for pressure head due to acceleration in the suction and delivery pipes of reciprocating pumps. (Nov/Dec 2016) 23. Discuss the working of gear pump using its schematic. (Apr/May 2017) PART – C 1.

A centrifugal pump running at 920 rpm and delivering 0.32 m 3/s of water against a head of

28 m , the flow velocity being 3m/s . If the manometric efficiency is 80% . Determine the diameter and width of impeller. The blade angle at outlet is 25º. (Apr/May 2015) 2.

The internal and external dia of an impeller of a centrifugal pump which is running at 1200

rpm are 300 mm and 600 mm. The discharge through the pump is 0.05m 3/s and the velocity of flow is constant and equal to 2.5 m/s. the diameter of the suction and delivery pipes are 150 mm and 100 mm respectively and suction and delivery heads are 6 m and 30 m of water. If the outlet vane angle is 45° and power required to drive the pump is 17 kW. Determine 1. Vane angle of the impeller at inlet. 2. Overall efficiency of the pump. 3. Manometric efficiency of the pump. (Nov/Dec 2016 & Nov/Dec 2017) 3.

The dimensionless specific speed of a centrifugal pump is .006. Static head is 32 m. Flow

rate is 50l/s. The suction and delivery pipes are each of diameter 15cm. The friction factor is 0.002. Total length is 60 m. other losses equal 4 times the velocity head in the pipe. The vanes are forward curved at120º. The width is one tenth of diameter . There is a 7 % reduction in flow areadue to blade thickness . The manometric efficiency is 80%. Determine the impeller diameter if inlet is radial (Nov/Dec 2015 & Nov/Dec 2017) 4.

An axial flow pump running at 620 rpm deliver 1.5m 3/s against a head of 5.2 m. The speed

ratio is 2.5. The flow ratio is 0.5. The overall efficiency is 0.8. Determine the power required and the blade angles at the root and tip and the diffuser blade inlet angle. Inlet whirl is zero. (May/June 2016) UNIT V TURBINES PART – A 1. Define hydraulic machines. Hydraulic machines which convert the energy of flowing water into mechanical energy. 2. Give example for a low head, medium head and high head turbine. Low head turbine – Kaplan turbine, Medium head turbine – Modern Francis turbine High head turbine – Pelton wheel

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3. What is impulse turbine? Give example. (Apr/May 2015) In impulse turbine all the energy converted into kinetic energy. From these the turbine will develop high kinetic energy power. This turbine is called impulse turbine. Example: Pelton turbine 4. What is reaction turbine? Give example. (Apr/May 2015) In a reaction turbine, the runner utilizes both potential and kinetic energies. Here portion of potential energy is converted into kinetic energy before entering into the turbine. Example: Francis and Kaplan turbine. 5. What is axial flow turbine? In axial flow turbine water flows parallel to the axis of the turbine shaft. Example: Kaplan turbine 6. What is mixed flow turbine? In mixed flow water enters the blades radially and comes out axially, parallel to the turbine shaft. Example: Modern Francis turbine. 7. What is the function of spear and nozzle? The nozzle is used to convert whole hydraulic energy into kinetic energy. Thus the nozzle delivers high speed jet. To regulate the water flow through the nozzle and to obtain a good jet of water spear or nozzle is arranged. 8. Define gross head and net or effective head. Gross Head: The gross head is the difference between the water level at the reservoir and the level at the tailstock. Effective Head: The head available at the inlet of the turbine. 9. Define hydraulic efficiency. (Nov/Dec 2012) It is defined as the ratio of power developed by the runner to the power supplied by the water jet. 10. Define mechanical efficiency. It is defined as the ratio of power available at the turbine shaft to the power developed by the turbine runner. 11. Define volumetric efficiency. (Nov/Dec 2015) It is defined as the vol. of water actually striking the buckets to the total water supplied by the jet. 12. Define overall efficiency. It is defined as the ratio of power available at the turbine shaft to the power available from water jet. 13. How will you classify the turbines? a. According to the type of energy at inlet.b. According to direction of flow through runner. b. According to the head at the inlet of turbine.d. According to the specific speed of the turbine. 14. Differentiate between the turbines and pumps. The hydraulic machines, which convert the hydraulic energy in to mechanical energy, are called turbines. The hydraulic machines, which convert the mechanical energy into pressure energy by means of centrifugal force is called centrifugal pump. St.Joseph’s College of Engineering

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15. Define specific speed of the turbine. (Apr/May 2015) Specific speed is the speed of a turbine which is identical in shape, geometrical dimensions, bladeanglesetc., with the actual turbine but of such a size that it will develop unit power when working under unithead. 16. What are the functions of draft tube? List the most commonly used draft tubes. (Nov/Dec 2017) a) It allows the turbine to be set above tail-water level, without loss of head, to facilitate inspectionand maintenance. b) It regains, by diffuser action, the major portion of the kinetic energy delivered to it from therunner. Most commonly used draft tubes: The straight conical or concentric tube, (2) The elbow type. 17. State and concise on Euler turbine equation (Nov/Dec 2015) Euler’s turbine equation plays a central role in turbo machinery as it connects the specific work and geometry and velocities in the impeller 18. Define plant efficiency of turbines. Efficiency of a plant is the percentage of the total energy content of a power plant's fuel that is converted into electricity. 19. Why does a Pelton wheel not possess any draft tube? In case of Pelton wheel the available head is converted into kinetic energy before entry to runner buckets and the turbine operate under atmospheric pressure conditions. The velocity of the water leaving at the turbine exit is small, therefore the exit of the runner is above the tail race level and there is no need for draft tube. 20. What are the different types of draft tubes? Conical draft tube, Simple elbow tubes, Moody spreading tubes, Elbow draft tubes with circular inlet and rectangular outlet. 21.List down the main components of pelton wheel. (May/June 2016) 1.Nozzle and flow regulating arrangement. 2.Runner and buckets. 3.Casing. 4.Breaking jet. 22. Diffrentiate between Kaplan and propeller turbine. (May/June 2016) The Kaplan turbine is a propeller-type water turbine which has adjustable blades. It was developed in 1913 by Austrian professor Viktor Kaplan, who combined automatically adjusted propeller blades with automatically adjusted wicket gates to achieve efficiency over a wide range of flow and water level. 23. Explain the type of flow in francis turbine. (Nov/Dec 2016) The Francis turbine is a type of water turbine that was developed by James B. Francis in Lowell, Massachusetts. It is an inward-flow reaction turbine that combines radial and axial flow concepts.

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24. What is draft tube? (Nov/Dec 2016) The draft tube is a conduit which connects the runner exit to the tail race where the water is being finally discharged from the turbine. The primary function of the draft tube is to reduce the velocity of the discharged water to minimize the loss of kinetic energy at the outlet. 25.How do you classify turbine based on flow direction and working medium. (Apr/May 2017) Classifications based on flow direction  Tangential flow: water flows in a direction tangential to path of rotational, i.e. Perpendicular  

to both axial and radial directions. Radial outward flow e.g : Forneyron turbine. Axial flow : Water flows parallel to the axis of the turbine. e.g: Girard, Jonval, Kalpan



turbine. Mixed flow : Water enters radially at outer periphery and leaves axially. e.g : Modern

Francis turbine. Classification based on working medium  Hydraulic Turbine and Gas Turbine 26.What is meant by Governing of turbines? (Apr/May 2017) Governing mechanism is used to regulate the water flow to the turbine at constant level so that the speed of the turbine is kept constant. This automatically regulates the quantity of water flowing through the runner in accordance with any variation of load. 27.Discuss the importance of Muschel curves. (Nov/Dec 2017) These are curves which are characteristic of a particular turbine which helps in studying the performance of the turbine under various conditions. These curves pertaining to any turbine are supplied by its manufacturers based on actual tests. The data that must be obtained obtained in testing a turbine are the following: 1. The speed of the turbine N, 2. The discharge Q, 3. The net head H, 4. The power developed P, 5. The overall efficiency η, 6. Gate opening PART -B 1. Derive an expression for maximum hydraulic efficiency in an impulse turbine. (Nov/Dec 2013) 2. Compare radial flow and axial flow turbo machines. 3. A Pelton wheel, working under a head of 500 m develops 13 MW when running at a speed of 430 rpm. If the efficiency of the wheel is 85%, determine the rate of flow through the turbine, the diameter of the wheel and the diameter of the nozzle. Take speed ratio as 0.46 and coefficient of velocity for the nozzle as 0.98. 4. A Pelton wheel works under a gross head of 510 m. One third of gross head is lost in friction in the penstock. The rate of flow through the nozzle is 2.2 m 3/sec. The angel of deflection of jet is 165°. Find the (i) power given by water to the runner (ii) hydraulic efficiency of Pelton wheel. Take CV = 1.0 and speed ratio = 0.45 5. A 137 mm diameter jet of water issuing from a nozzle impinges on the buckets of a Pelton wheel and the jet is deflected through an angle of 165 by the buckets. The head available at the

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nozzle is 400m. Find: (a) Force exerted on the buckets and (b) Power developed. Assume C v as 0.97, speed ratio as 0.46 and reduction in velocity while passing through the buckets as 15%. 6. A Pelton turbine is required to develop 9000 KW when working under a head of 300 m the impeller may rotate at 500 rpm. Assuming a jet ratio of 10 and an overall efficiency of 85% calculate (i) Quantity of water required, (ii) Diameter of the wheel, (iii) No of jets, (iv) No and size of the bucket vanes on the runner 7. A pelton wheel turbine develops 3000kW power under a head of 300m. The overall efficiency of the turbine is 83%. If the speed ratio = 0.46, Cv = 0.98 and specific speed is 16.5, then find diameter of the turbine and diameter of the jet. 8. A pelton wheel has a mean bucket speed of 10m/s with a jet of water flowing at the rate of 700 lps under a head of 30m. The buckets deflect the jet through an angle of 160deg. Calculate power given by the water to the runner and the hydraulic efficiency of the turbine. Assume coefficient of velocity as 0.98. 9. A reaction turbine works at 450 r.p.m. under a head of 120 m. Its diameter at inlet is 1.2 m and the flow area is 0.4 m2. The angles made by absolute and relative velocities at inlet are 20 and 60 respectively with the tangential velocity. Determine: (i)the volume rate of flow, (ii) the power developed, and (iii) the hydraulic efficiency. 10. The velocity of whirl at inlet to the runner of an inward flow reaction turbine is 3.15 and the velocity of flow at inlet is 1.05

H

m/s. The velocity of whirl at exit is 0.22 H

same direction as at inlet and the velocity of flow at exit is 0.83

H

H

m/s

m/s in the

m/s, where H is head of water

30 m. The inner diameter of the runner is 0.6 times the outer diameter. Assuming hydraulic efficiency of 80%, compute angles of the runner vanes at inlet and exit. 11. A Kaplan turbine develops 24647.6kW power at an average head of 39m. Assuming the speed ratio of 2, flow ratio of 0.6, diameter of the boss equal to 0.35 times the diameter of the runner and an overall efficiency of 90%, calculate the diameter, speed and specific speed of the turbine. (Nov/Dec 2015 & Apr/May 2017) 12. Discuss about draft tube and its types. Discuss about Kaplan turbine with a neat sketch. (Apr/May 2015) 13. Describe the efficiencies of the turbine. (Nov/Dec 2016) 14. Explain the working of Kaplan turbine. Construct its velocity triangle. (Nov/Dec 2016) 15. Explain the performance Characteristics curves of turbine. (Apr/May 2017)

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PART – C 1. The following data is given for francis turbine : Net head = 60 m, speed = 700 rpm, shaft power = 294.3 kW, ƞₒ= 84%. ƞ h = 93 %, flow ratio = 0.2, breadth ratio = 0.1, outer diameter of the runner = 2 inner diameter of the runner. The thickness of vanes occupies 5% of the circumferential area of the runner. Velocity of flow is constant at inlet and outlet and discharge is radial outlet. Determine : 1. The guide blade angle, 2. Runner vane angle the inlet and outlet. 3. Diameter of the runner at inlet and outlet. 4. Width of the wheel at the inlet. (Nov/Dec 2016&Apr/May 2017) 2. A Kaplan turbine delivering 40 MW work under a head of 40 m. And runs at a speed of 150 rpm,the hub diameter is 6m. The overall efficiency is 90%. Determine the blade angles of the hub and tip also at a dia of 4m. also find the speed ratio and flow ratio based on tip velocity. Assume hydraulic efficieny as 95%

. (May/June 2016)

3. A Francis turbine developing 16120 kW under a head of 260m runs at 600rpm. The runner outside diameter is 1500mm, width 135mm, flow rate 7m 3/s. The exit velocity of draft tube outlet, whirl velocity is 0 at exit. Neglect blade thickness. Determine overall and hydraulic efficiency and rotor blade angle at inlet. Also find guide vane outlet angle. (Apr/May 2015 & Nov/Dec 2017) 4. At a location selected to install a hydro electric power plant, the head estimated as 540 ms. The flow rate was determined as 22 m 3/s. The plant is located at a distance of 2 km from the entry to the penstock pipes along the pipes. Two pipes of 2 m diameter are proposed with a frictional factor of 0.03. Additional loses amount to about 1/4th of frictional loss. Assuming an overall efficiency of 85%, determine how many single jet unit running at 330 rpm will be required. (May/June 2016) 5. A hub diameter of a Kaplan turbine, working under a head of 12m, is 0.35 times the diameter of the runner. The turbine is running at 100rpm. If the vane angle of the runner at outlet is 15deg. And flow ratio 0.6, find (i) diameter of the runner, (ii) diameter of the boss, and (iii) Discharge through the runner. Take the velocity of whirl at outlet as zero. (Nov/Dec 2015 & Nov/Dec 2017)

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