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Particulars

Page Number

1 Scheme 3

2 Syllabus 4

3 Lecture Plan 6

4 List of Books 9

5 Tutorial Sheets -

6 Assignments 10

7 MID Question Papers 25

8 Model Question Paper 26

9 Gtu Question Paper 27

3

Course of Study and Scheme of Examination for Batch starting from December 2018

B.E-4th Semester (MECHANICAL ENGINEERING)

Teaching Scheme Credit Examination Marks

Total Marks L T P C

Theory Marks Practical Marks ESE(E) PA(M) ESE(V) PA(I) PA ALA ESE OEP

4 0 2 6 70 20 10 20 10 20 150

4

SSYYLLLLAABBUUSS

UNIT-I Fluids and Their Properties : Introduction of fluid, fluid classifications, hypothesis of continuum, Shear stress in a moving fluid, molecular structure of material, fluid density, viscosity, causes of viscosity in gases and liquids, surface tension, capillary effect, vapor pressure, cavitation, compressibility and the bulk modulus

UNIT-II Pressures and Head: Types of Pressure, Pascal’s law of pressure at a point, variation of pressure vertically in a fluid under gravity, equality of pressure at the same level in a static fluid, general equation for the variation of pressure due to gravity from a point to point in a static fluid, pressure and head, the hydrostatic paradox, pressure measurements using Elastic Pressure Transducers, Force Balance Pressure gauge, Electrical Pressure Transducers

UNIT-III Static Forces on Surface and Buoyancy: Fluid static, action of fluid pressure on surface, resultant force and center of pressure on a plane surface under uniform pressure, resultant force and center of pressure on a plane surface immersed in a liquid, pressure diagrams, forces on a curved surface due to hydrostatic pressure, buoyancy, equilibrium of floating bodies, stability of a submerged body, stability of floating bodies, determination of the metacentric height, determination of the position of the metacentre relative to the center of buoyancy.

UNIT-IV Motion of Fluid Particles and Streams: Fluid flow, different types of flow, frames of reference, analyzing fluid flow, motion of a fluid particle, acceleration of a fluid particle, discharge and mean velocity, continuity of flow, continuity equations for 2-D and 3-D flow in Cartesian coordinates of system .

UNIT – V The Energy Equation and its Application: Momentum and fluid flow, Momentum equation for 2-D and 3-D flow along a stream line, momentum correction factor, Euler’s equation of motion along a stream line, Mechanical energy of a flowing fluid –Bernoulli’s theorem, kinetic energy correction factor, pitot tube, determination of volumetric flow rate via pitot tube, changes of pressure in tapering pipe, principle of venturimeter, pipe orifices, theory of small orifices discharging to atmosphere, theory of large orifices, Rotameter, elementary theory of notches and weirs, flow in a curved path

UNIT – VI Two-Dimensional Ideal Fluid Flow: Rotational and ir-rotational flow, circulation and vorticity, streamlines and the stream functions, velocity potential and potential flow, relation between stream function and velocity potential; flow nets, stream function and velocity potential for uniform flow, vortex flow.

UNIT – VII Dimensional Analysis And Similarities: Dimension reasoning, dimensional homogeneity, dimensional analysis using Rayleigh’s method, Buckingham π-theorem, significance of dimensionless, use of dimensionless numbers in experimental investigation, geometric similarity, dynamic similarity, Kinematic similarity, model testing-Model laws, Undistorted and Distorted models.

Category of Course

Course Title Course Code Theory Paper L T P

Mechanical Fluid Mechanics 2141906 4 0 2 70

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UNIT – VIII Viscous Flow: Reynolds number and Reynolds experiment, flow of viscous fluid through circular pipe- Hagen Poiseuille formula, Flow of viscous fluid between two parallel fixed plates, power absorbed in viscous flow through - journal, foot step and collar bearing , movement of piston in dash pot, methods of measurement of viscosity.

UNIT – IX Turbulent Flow: Expression for coefficient of friction -Darchy Weishbach Equation, Moody diagram resistance of smooth and rough pipes shear stress and velocity distribution in turbulent flow through pipes.

UNIT – X Flow through pipes: Major energy losses, Minor energy losses, Hydraulic gradient and total energy lines, Pipes in series and parallel, Equivalent pipes, Siphon, power transmission through pipe, Flow through nozzle at end of pipe, Water hammer in pipes

UNIT – XI Compressible Flow: Basic equations for one dimensional compression, Pressure wave propagation, sound velocity in fluid, Mach number, Stagnation properties .

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LECTURE PLAN

Lect Topics to be covered Teaching hours

1 Introduction of fluid, fluid classifications fluid density, viscosity, causes of viscosity in gases and liquids

1

2 surface tension, capillary effect, vapor pressure, cavitations, compressibility and the bulk modulus

1

3 Examples 1

4 Types of Pressure, Pascal’s law of pressure at a point, variation of pressure vertically in a fluid under gravity,

1

5 equality of pressure at the same level in a static fluid, general equation for the variation of pressure due to gravity from a point to point in a static fluid

1

6 pressure and head, the hydrostatic paradox, 1

7 pressure measurements using Elastic Pressure Transducers 1

8 Force Balance Pressure gauge, Electrical Pressure Transducers 1

9 Fluid static, action of fluid pressure on surface, 1

10 resultant force and center of pressure on a plane surface under uniform pressure

1

11 resultant force and center of pressure on a plane surface immersed in a liquid, pressure diagrams,

1

12 forces on a curved surface due to hydrostatic pressure, buoyancy, 1

13 equilibrium of floating bodies, stability of a submerged body, 1

14 stability of floating bodies, determination of the metacentric height, 1

15 determination of the position of the metacentre relative to the center of buoyancy

1

16 Examples 1

17 Fluid flow, different types of flow, frames of reference, analyzing fluid flow

1

18 motion of a fluid particle ,acceleration of a fluid particle, discharge and mean velocity, continuity of flow

1

19 Continuity equations for 2-D and 3-D flow in Cartesian coordinates of system.

1

20 Examples 1

21 Momentum and fluid flow, Momentum equation for 2-D and 3-D flow along a stream line, momentum correction factor,

1

22 Momentum and fluid flow, Momentum equation for 2-D and 3-D flow along a stream line, momentum correction factor, Euler’s equation of motion along a stream line, Bernoulli’s theorem

1

23 pitot tube, determination of volumetric flow rate via pitot tube, changes of pressure in tapering pipe, principle of venturimeter, pipe orifices

1

7

24 theory of small orifices discharging to atmosphere, theory of large orifices 1

25 Rota meter , Examples 1

26 elementary theory of notches and weirs

1

27 flow in a curved path

1

28 Examples 1

29 Rotational and ir-rotational flow, circulation and vorticity, streamlines and the stream functions

1

30 velocity potential and potential flow, relation between stream function and velocity potential

1

31 flow nets, stream function and velocity potential for uniform flow, vortex flow

1

32 Examples 1

33 Dimension reasoning, dimensional homogeneity, dimensional analysis using Rayleigh’s method,

1

34 Buckingham π-theorem, significance of dimensionless, use of dimensionless numbers in experimental investigation

1

35 geometric similarity, dynamic similarity, Kinematic similarity 1

36 model testing-Model laws ,Undistorted and Distorted models 1

37 Examples

1

38 Reynolds number and Reynolds experiment, flow of viscous fluid through circular pipe- Hagen Poiseuille formula 1

39 Flow of viscous fluid between two parallel fixed plates, 1

40 power absorbed in viscous flow through - journal 1

41 foot step and collar bearing , example 1

42 Movement of piston in dash pot, methods of measurement of viscosity. 1

43 Examples

1

44 Expression for coefficient of friction -Darchy Weishbach Equation,

1

45 Moody diagram resistance of smooth and rough pipes shear stress 1

46 Velocity distribution in turbulent flow through pipes. 1

47 Examples 1

48 Major energy losses, Minor energy losses, 1

49 Hydraulic gradient and total energy lines, 1

50 Pipes in series and parallel, Equivalent pipes, Siphon, 1

51 power transmission through pipe, 1

8

52 Flow through nozzle at end of pipe, Water hammer in pipes

1

53 Example

1

54 Basic equations for one dimensional compression, 1

55 Pressure wave propagation, sound velocity in fluid, 1

56 Mach number, Stagnation properties 1

9

REFERENCE BOOK

S. No. TITLE AUTHOR PUBLISHER / EDITION

1 Fluid Mechanics and Fluid Power Engineering

D.S. Kumar

S.K.Kataria & Sons

2 Fluid Mechanics and Hydraulic Machines R.K. Bansal, Laxmi Publications

3 Fluid Mechanics and Hydraulic

Machines R. K. Rajput S.Chand & Co.

10

ASSIGNMENT TOPICS

S. No. TOPIC

1 Fluids and Their Properties

2 Pressures and Head

3 Static Forces on Surface and Buoyancy

4 Motion of Fluid Particles and Streams

5 The Energy Equation and its Application 6 Two-Dimensional Ideal Fluid Flow

7 Dimensional Analysis And Similarities

8 Viscous Flow

9 Turbulent Flow

10 Flow through pipes

11 Compressible Flow

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Assignment 1: Fluids and Their Properties

Sr. No. Name of Question

1 Density, Specific volume, Weight density, Surface tension, Capillarity.

2 Viscosity, Kinematic viscosity, Cohesion, Adhesion

3 Write a short note on Kinetic energy correction factor.

4 Explain the phenomenon of capillarity. Obtain and expression for capillary rise and capillary fall of a liquid.

5 What is the difference between dynamic viscosity and kinematic Viscosity? State their units

6 Obtain an expression for capillary rise of liquid

7 Define capillarity and develop a formula for capillary rise of a liquid Between two concentric glass tubes with usual notations. State and explain Newton’s law of viscosity.

8 Viscosity, Surface tension, Specific weight, Newtonian fluid, Ideal fluid

9 Specific weight, cohesion, capillarity, ideal fluid.

10 What do you understand by continuum concept of a fluid?

11 At a depth of 9 km in the ocean, the pressure is 9.5*104 kN/m2. The specific weight of the ocean water at the surface is 10.2 kN/m3 and its average Bulk modulus is 2.4*106 kN/m2. Determine: - (i) The change in specific volume, (ii) The specific volume at 9 km depth and (iii) The specific weight at 9 km depth

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ASSIGNMENT -2 Pressures and Head

Sr. No. Name of Question

1 What do you mean by gauge pressure, vacuum pressure and absolute pressure? Explain the working principle of U-tube differential manometer with neat sketch.

2 State and prove Pascal’s law for static fluid.

3 Prove that “Intensity of pressure at any point in a fluid at rest is same in all direction.”

4 State and prove Pascal’s law. Also mention its application.

5 Describe vertical single column manometer? How will you measure the fluid pressure with it?

6 State Pascal’s law and hydrostatic law.

7 State and prove Pascal’s law.

8 Enlist types of manometers. Differentiate between u-tube manometer and u-tube differential manometer

9 Define atmospheric pressure, gauge pressure and absolute pressure. State and prove Pascal’s Law with usual notations

10 Define manometer. List different types of manometer. Explain single column Manometer with usual notation. State advantages and limitations of manometer

11 Explain 1.bourden tube pressure gauge. 2. Diaphragm gauge.

12. Obtain expression for loss of head due to friction in pipe flow.

13 Enlist different types of manometers and explain the working of a differential U-tube manometer i) Distinguish between ‘absolute pressure’ and ‘gauge pressure.

14 A U-tube manometer is used to measure the pressure of 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 water and mercury is in the left limb. Determine the pressure of water in the main line, if the difference in level of mercury in the limbs of U-tube is 12cm and the free surface of mercury is in level with the centre of the pipe. If the pressure of water in pipe line is reduced to 9810 N/m2. Calculate the new difference in the level of mercury.

15 The water is flowing through a taper pipe of length 100 m having diameter 600 mm at the upper end and 300 mm at the lower end, at the rate of 50 litres/sec. The pipe has a slope of 1 in 30. Find the pressure at the lower end if the pressure at the higher level is 19.62 * 104 N /m2 & lower end is 10 m above datum.

16 Calculate the pressure exerted by 5 kg of nitrogen gas at a temperature of 10ºc if the volume is 0.4cubic meter. Molecular weight of nitrogen is 28.Assume ideal gas laws are applicable. take universal gas constant (MR) = 8314 Nm/kg-mole-K

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ASSIGNMENT -3 Static Forces on Surface and Buoyancy

Sr. No. Name of Question

1 Force of buoyancy, Metacentre, Total pressure, Centre of pressure

2 Derive the expression for total pressure and centre of pressure for a vertical plate submerged in the liquid with usual notations.

3 Explain the condition of stability for a submerged body.

4 Explain force on a curved surface due to hydrostatic pressure. Derive an expression of resulting horizontal, vertical and resultant force on a curved surface immersed in a liquid.

5 Show that the distance between the meta-centre and center of buoyancy is given by BM=I/∀.

6 What is compressibility? Derive an expression for it.

7 Prove that the centre of pressure for any immersed surface always lies below its centroid.

8 Enlist types of manometers. Differentiate between u-tube manometer and u-tube differential manometer.

9 Define buoyant force, center of buoyancy, met center and met centric height. Also describe conditions of equilibrium for floating and submerged bodies.

10 Define multicenter and met centric height. Explain method for determination of met centric height

11 For inclined immersed surface derive with usual notations, expression for total pressure and center of pressure

12 Explain the terms: Rotational flow, relative equilibrium, buoyant force

13 ‘Buoyant force’. Discuss different stability conditions for a floating body.

14 Derive equation for total pressure and centre of pressure for vertically immersed surface.

15 A solid cylinder of diameter 4 m has a height of 4 m. Find the met centric height of the cylinder if the specific gravity of the material of cylinder is 0.7 and it is floating in water with its axis vertical. State whether the equilibrium is stable or unstable.

16 A body has the cylindrical upper portion of 4m diameter and 2.4m deep. The lower portion, which is curved, displaces a volume of 800 litres of water and its centre of buoyancy is situated 2.6m below the top of the cylinder. The centre of gravity of the whole body is 1.6m below the top of the cylinder and the total displacement of water is 52 kN. Find the metacentric height of the body.

17 A wooden block of specific gravity of 0.7 and dimensions 18 cm wide, 30 cm deep and 100 cm long floats horizontally on 18 cm wide surface in water. Calculate the metacentric height and comment on the stability of the block. If the block is given a tilt of 6o in the clockwise direction. Calculate what should be the mass should be kept at a distance from the centre 5 cm on the opposite side of offset the tilt.

18 Determine the total pressure on a circular plate of diameter 1.5 m which is placed vertically in water in such a way that the centre of the plate is 3 m below the free surface of water. Find the position of centre of pressure also.

19 A pontoon of 15696 KN displacements is floating in water a weight of 245.25 KN is moved through a distance of 8 m across the deck of pontoon which tilts the pontoon through an angle of 4° find the

14

metacentric height of the pontoon.

20 square plate of diagonal 2m is immersed in a liquid with its diagonal vertical and upper corner is 0.5m below the free surface of the liquid. The specific gravity of the liquid is 1.4. Find, (i) The force exerted by liquid on the plate. (ii) The position of its centre of pressure

21 A solid cylinder 2.5m in diameter and 2.5m high is floating in water with its axis vertical. If the specific gravity of cylinder material is 0.7, Find metacentric height. Also state whether the equilibrium is stable or unstable.

15

ASSIGNMENT -4 Motion of Fluid Particles and Streams

Sr. No. Name of Question

1 Derive continuity equation in 3 dimensional co-ordinate system 2 Explain briefly : Steady flow and unsteady flow

Uniform flow and non uniform flow Laminar and turbulent flow

4 Define: - (i) path line (ii) stream line (iii) stream tube 5 State the characteristics of Laminar flow and Turbulent flow 6 Derive an expression for continuity for 3-D flow and reduce it for steady, incompressible 2-D flow in

Cartesian coordinate system. 7 Derive an expression for continuity for three dimensional flows and reduce it for steady,

incompressible two dimensional flows. 8 What do you mean by equipotential line and a line of constant stream Function 9 Define stream function and velocity potential function. 10 Define continuously equation and derive an expression for a three dimensional flow. 11 Compressible flow and Incompressible flow

(ii) Uniform flow and Non-uniform flow 12 Obtain an expression for continuity equation for a three dimensional flow.

13 Explain briefly: 1. steady and unsteady flow

2.Uniform and non-uniform flow 3.rotational and irrotational flow

14 Define rate of flow. Derive continuity equation.

15 Differentiate between streamline and equipotential line. For a 2-D flow field, the velocity potential is given as _ = 2xy – x. Determine the stream function _ at a point P (2, 2).

16 Derive an expression for continuity for 3-D flow and reduce it for steady incompressible 2-D flow in Cartesian coordinate system.

17 Velocity components of a fluid flow are given as u = (6xy2 + t), v = (3yz + t2 + 5), w = (z + 3 ty), where x, y, z are given in meters and time t in seconds. Determine velocity vector at point P (4, 1, 2) at time t = 4 seconds. Also determine the magnitude of velocity and acceleration of the flow for given location and time.

18 Two parallel plates 80 mm apart have laminar flow of oil between them with maximum velocity of flow is 1.5 m/s. Calculate : (I) Discharge per meter width (II) Shear stress at the plate (III) The difference in the pressure between two points 20 meter apart. (IV) Velocity gradient at the plates. (V) Velocity at 20 mm from the plate. Assume viscosity of oil 24.5 poise.

19 Two parallel plates kept 100 mm apart have laminar flow of oil between them. Maximum velocity of flow is 1.5 m/sec. Calculate 1). Discharge per meter width 2). Shears stress at the plate 3). Difference in pressure between two point 20 meter apart 4). Velocity gradient of plates 5). Velocity at 20 mm from the plates

16

20 A laminar flow is taking place in a pipe of diameter of 200 mm. The maximum velocity is 1.5 m/sec. Find the mean velocity and the radius at which this occurs. Also calculate the velocity at 4 cm from the wall of the pipe.

17

ASSIGNMENT -5 The Energy Equation and its Application

Sr. No. Name of Question

1. With usual notations derive the expression for the discharge through a triangular notch and for rectangular notch.

2. Derive Bernoulli’s equation and clearly state the assumption made.

3. Derive expression for discharge through pipe orifice.

4. What are the advantages of triangular notch over rectangular notch? (ii) Find an expression for the discharge over a rectangular notch.

5. Define Kinetic Energy correction factor and momentum correction factor.

6. Explain the construction and working of a Venturimeter and also derive an expression for the discharge through it.

7. Compare a triangular notch with a rectangular notch for measuring discharges and derive an expression for the discharge through a triangular notch.

8. Derive an expression for the measurement of velocity of flow at any point in a pipe or channel by Pitot tube.

9. Explain large orifice and derive expression for discharge through large orifice.

10. Explain: Vena-contract. Discuss the characteristics of flow at vena-contracts, in case of an orifice.

11. Momentum principle. What are its applications?

12. Derive expression of time of emptying a tank through an orifice at its bottom.

13. Derive expression of time of emptying a hemispherical tank through an orifice at its bottom.

14. A horizontal venturimeter of 200 mm X 100 mm is used to measure the discharge of an oil of specific gravity 0.85. A mercury manometer is used for the purpose. If the discharged is 100 litres per second and if the coefficient of discharge of the venturimeter is 0.97, find the difference of mercury level in between two limbs of manometer.

15 The inlet and throat diameters of a vertically mounted venturimeter are 30 cm and 10 cm respectively. The throat section is below the inlet section at a discharge of 10 cm. The specific gravity of the liquid is 900 Kg/m3. The intensity of pressure at inlet is 140 KPa and the throat\ pressure is 80 KPa. Calculate the flow rate in Lps. Assume that 2 % of the differential head is lost between inlet and throat. Take coefficient of Discharge 0.97.

16 A horizontal Venturimeter with inlet diameter 20cm and throat diameter 10cm is used to measure the flow of oil of sp.gr 0.8. The discharge of oil through venturimeter is 60 Liters/Second. Find the reading of the oil mercury differential manometer take Cd = 0.98.

17 A pipe of 1.4m in diameter is required to transport an oil of specific gravity 0.8 and dynamic viscosity 0.04 poise at the rate of 2500 liters per second. Test was conducted on a150mm diameter pipe using water at 20˚C. The viscosity of water at 20˚C is 0.01 poise. Find the rate of flow in the model.

18 A tank has two identical orifices in one side of the vertical side. the upper orifice is 2 m below the water surface and the lower orifice is 4 m below the water surface. if the value of Cv for both

18

orifice is 0.9, find the point of intersection of two jets.

19 a circular tank of diameter 4m contains water to a depth of 5m. the tank is provided with an orifice of dia 0.5m at the bottom. find the time taken by water, (i) to fall from 5m to 2m and (ii) for completely emptying the tank.

19

ASSIGNMENT -6 Two-Dimensional Ideal Fluid Flow

Sr. No. Name of Question

1 Defines:1.Stream function ( ψ ) 2. Velocity potential function ( O ) 3. Circulation ( Ґ ) 4. Flow net

2 Prove that the velocity at the outlet of nozzle for maximum flow rate equals sonic velocity.

3 Derive an expression of stream function and velocity potential function for vortex flow.

4 Define and explain circulation. What is the importance of concept of circulation?

5 Explain Flow-net and state the importance of flow net.

6 Define circulation. Prove that circulation = ∫dA with usual Notations.

7 Distinguish between forced vortex and free vortex flow.

8 Define circulation and velocity potential function. Explain flow net and state the important of flow net

9 Certain mass of air is passing through a horizontal pipe with a velocity of 350 m/s, at a section with corresponding pressure of 80 KN/m2 absolute and temperature 45oC. There is a change in diameter of the pipe at a section and pressure at this section is 128 KN/m2, absolute. Find the velocity of air stream if the flow is adiabatic.

20

ASSIGNMENT -7 Dimensional Analysis and Similarities

Sr. No. Name of Question

1 Define the following dimensionless numbers: (I) Reynold’s No. (II) Froude No. (III) Euler’s No. (IV) Mach No.

2 The pressure difference Δp in a pipe of diameter D and length L due to Turbulent flow depends on velocity V, viscosity μ, density ρ and roughness k. Using Buckingham’s π-theorem obtain an expression for Δp.

3 Using Buckingham’s π-theorem, show that the lift FL on airfoil can be Expressed as FL=ρV2d2Ф [(ρVd/_), α]. Where, ρ= mass density V= velocity of flow, d=characteristic depth =co-efficient of viscosity and α=angle of incidence

4 State Buckingham’s π-theorem. How the repeating variables are selected in dimensional analysis? 5 Derive on the basis of dimensional analysis suitable parameters to present the thrust developed by

propeller. Assume that thrust P depends upon the angular velocity , speed of advance V, diameter D, dynamic viscosity , mass density , elasticity of the fluid medium which can be denoted by speed of the sound in the medium C.

6 State similarity laws. Where are they used? Explain Froude, Euler and Weber model law with applications.

7 Derive Euler’s equation of motion along a streamline

8 What is meant by geometric, kinematic , and dynamic similarities 9 State Buckingham’s Π theorem method.. What do you mean by repeating Variables 10 Derive Euler’s equation of motion along a stream line for an ideal fluid and integrate it to get the

Bernoulli’s equation 11 The efficiency η of a fan depends on the density ρ, the dynamic viscosity μ of the fluid, the angular

velocity ω, diameter D and discharge Q. Express efficiency η in terms of dimensionless parameters by using Buckinghams-π thorem.

12 State the various dimensionless numbers with their significance in fluid flow situations

13 Discuss different types of similarities that must exist between a prototype and its model

14 The pressure difference Δp in a pipe of diameter d and length L due to viscous flow, depends on velocity v,viscosity μ and density ρ. Using Buckingham’s π-theorem, obtain an expression for Δp.

15 Explain ‘Bernoulli’s theorem’. What are the assumptions in Bernoulli’s theorem?

16 Show, using Buckingham’s π theorem, that the resistance (F) to the motion of a sphere of diameter (D) moving with a uniform velocity (V) through a real fluid of density (ρ) and viscosity (μ) is given by:

17 Reynolds number. Also, explain “Reynolds’ model law”

18 Define Reynolds’s number and give its significant. Explain reynold experiment with neat sketch.

19 Explain Euler’s, Weber and mach model law.

20 Explain Buckingham’s Π – theorem for dimensional analysis.

21

Assignment-8 Viscous Flow

Sr. No. Name of Question

1 Derive the expression for shear stress and velocity distribution for the flow of viscous fluid through circular pipe with usual notations.

2 Derive an expression for velocity distribution for viscous flow through a circular pipe. Also sketch the velocity distribution and shear stress distribution across the section of a pipe

3 What is Hagen Poiseuille’s formula? Derive an expression for Hagen Poiseuille’s formula.

4 Derive an expression for Hagen Poiseuille’s theorem

5 State the characteristics of a viscous flow

6 Derive an expression for power absorbed in overcoming viscous resistance in case of a journal bearing.

7 Obtain relationship between shear stress and pressure gradient for laminar flow

22

Assignment-9 Compressible Fluid Flow

Sr. No. Name of Question

1 Prove that velocity of sound wave in a compressible fluid is given by C=√(k/ρ) Where k= Bulk modulus of fluid and ρ = Density of fluid.

2 With the help of diagram, explain relationship between mass flow rate and pressure ratio for compressible flow

3 Explain Zone of action, Zone of silence, Mach angle and Mach-cone with the help of diagram

4 Prove that the velocity of sound wave in compressible fluid is given by C=√K/ρ.

5 What is compressibility? Derive an expression for it

6 Prove that the velocity of sound waves in a compressible fluid is given by C = √ (k/ρ). K= Bulk modulus. ρ = Mass Density

7 Sub-sonic flow, Super-sonic flow, Mach angle and Mach cone.

8 State assumptions for Bernoulli’s equations. Derive Bernoulli’s equations

9 Calculate the stagnation pressure temp. and density on the stagnation point on the nose of the plane which is flying at 800 km/hr through still air having a pressure 8 N/square cm (abs) and temp. – 10 º c. Take R = 287 J/Kg –K, γ = 1.4

23

Assignment-10 TURBULENT FLOW:

Sr. No. Name of Question

1 What is velocity defect? Derive an expression for the velocity defect for turbulent flow in pipes.

2 Write a short note on moody diagram for calculating the head loss due to friction.

3 Define turbulent flow, and compare with laminar flow.

4 Explain characteristics of turbulence flow.

5 Derive Darcy weisbach equation for the co-efficient of turbulence.

6 Derive co-efficient of friction in terms of shear stress.

7 Explain fully turbulent floe.

8 Derive an expression for universal velocity distribution for turbulent floe.

9 Drive an expression for universal velocity distribution in terms of average velocity for through flow through smooth and rough pipes.

10 Prove that the difference of local velocity and average velocity for turbulent flow through rough or smooth pipes.

11 What is velocity defect? Derive an expression for velocity defect in pipes.

12 Explain the Moody diagram.

24

Assignment-11 FLOW THROUGH PIPES Sr. No. Name of Question

1 What do you understand by the terms major energy loss and minor energy losses in pipe? Derive Darcy-Weisbach equation with usual notations

2 Derive expression for finding loss of head due to (i) sudden enlargement (ii) sudden contraction.

3 Explain briefly HGL and TEL.

4 Derive an expression for the power transmission through the pipes. find also the condition for maximum transmission of power and efficiency.

5 Find the head loss due to friction in a pipe of diameter 200mm and length 60m, through which water is flowing at a velocity of 2.5m/s using Darcy-Weisbach formula. take f=0.005

6 In a pipe of diameter 200mm and length 500m , an oil of sp.gravity 0.9 and viscosity 0.06 poise is flowing at a rate of 0.06 m3/s. find 1) the head loss due to friction . 2) power required to maintain the flow.

7 A horizontal pipe of 100 mm dia is joined by sudden enlargement to a 150 mm dia pipe. water is flowing through it at the rate of 2 m3/s. Find 1) loss of head due to enlargement and 2) pressure diff in two pipes.

8 A horizontal pipe line 50m long is connected to a water tank at one end and discharge into atmosphere at the other end. For the first 30 m of its length from the tank the pipe is 200 mm in diameter and its diameter is suddenly enlarge to 400 mm. the height of water level in the tank is 10 m above the center of pipe. determine the rate of flow considering all losses of head which occur Take f=0.01 for both section of pipe.

9 Two resevoirs A and C having a difference of level of 18 m are connected by a pipeline ABC, the elevation of point B being 4 m below the level of water in reservoir A. the length of AB pipe is 250 m the pipe being made of mild stell having friction factor f1, while the length of BC is 450 m. the pipe is made of cast-iron of friction factor f2.Both the length AB and BC have a dia of 200 mm . a partially closed valve is located in the length BC at a distance of 150 m from reservoir C. if the flow through the pipe is 3 m3/s, the pressure head at B is 0.5 m and head loss at the valve is 5m. (1) friction factor f1 and f2 (2) draw HGL and TEL . consider loss of head at entrace and exit.

25

Laxmi Institute of Technology , Sarigam Approved by AICTE, New Delhi; Affiliated to Gujarat Technological University, Ahmedabad

Academic Year 2018-19 Centre Code: 086 Examination : MID-1-EXAM-2019 Branch: Mechanical/Automobile Semester: 4 Sub Code: 2141906 Sub: FLUID MECHANICS Date: 01/02/2019 Time: 9:00-10:00 AM Marks: 20 Q1

Explain the phenomenon of capillarity. Obtain an expression for capillary rise and capillary fall of a liquid.

OR 5

Q1 Derive an equation of pressure variation with respect to vertical axis in a fluid under the gravity. 5

Q2 A 50 mm diameter shaft rotates with 500 rpm in a 80 mm long journal bearing with 51 mm internal diameter. The annular space between the shaft and bearing is filled with lubricating oil of dynamic viscosity 1 poise. Determine the torque required and power absorbed to overcome friction.

OR

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Q2 At a depth of 9 km in the ocean, the pressure is 9.5*104 kN/m2. The specific weight

of the ocean water at the surface is 10.2 kN/m3 and its average Bulk modulus is 2.4*106 kN/m2. Determine: - (i) The change in specific volume, (ii) The specific volume at 9 km depth and (iii) The specific weight at 9 km depth Derive Euler’s equation of motion.

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Q4 A horizontal venturimeter with inlet diameter 150 mm and throat diameter 75 mm is employed to measure the discharge of water. The differential manometer connected to the inlet gives reading of 150 mm of mercury. Determine the rate of flow if the co-efficient of discharge is 0.98.

OR

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Q4

A pipe line carrying oil of specific gravity 0.9, changes in diameter from 250 mm diameter at a position 1 to 450 mm diameter at a position 2 which is 6 meters at a higher level. If the pressure at 1 and 2 are 12 N/cm2 and 6 N/cm2 respectively and the discharge is 250 liters/s. Calculate the loss of head and direction of flow.

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