LOK NAYAK JAI PRAKASH INSTITUTE OF TECHNOLOGY

CHAPRA

COURSE FILE

OF FLUID MECHANICS

(ME 203)

Faculty Name: PRAVIN RAI

ASST. PROFESSOR, DEPARTMENT OF MECHANICAL ENGINEERING

CONTENTS 1. Cover Page & Content

2. Vision of the Department

3. Mission of the department

4. PEOs and POs

5. Course objectives & course outcomes (COs)

6. Mapping of COs with POs

7. Course Syllabus and GATE Syllabus

8. Time table

9. Student list

10. Course Handout

11. Lecture Plan

12. Assignment sheets

13. Tutorial Sheets

14. Sessional Question Papers

15. Old End Semester Exam (Final Exam) Question Papers

16. Question Bank

17. Power Point Presentations

18. Lecture Notes

19. Reference Materials

20. Results

21. Result Analysis

22. Quality Measurement Sheets

a. Course End Survey

b. Teaching Evaluation

23. CO-PO Attainment

Vision and Mission of Mechanical Engineering Department

Vision

The Mechanical Engineering department visions to be known globally in the field of technical education and to overcome the issues of industry and society.

Mission

1. To deliver outcome based education to undergraduate students 2. To establish an environment for students where they can build professional

and personal integrity to pursue long productive career. 3. To maintaining state of the art research facilities to provide collaborative

environment that stimulates faculty, staff and students with opportunities to create, analyze, apply and disseminate knowledge.

4. To equip students with good academic, corporate and entrepreneurship skills as well as create global awareness in them required by engineering profession

Program Educational Objectives

1. To prepare the students for successful career in industries, entrepreneurship or in higher studies.(Preparation)

2. To inculcate engineering attitude to analyze, design and solve real life engineering problems.(Core knowledge)

3. To promote the students for continuous learning, with strong professionals, ethical and moral values.(Learning Environment)

Program Specific Outcomes

The graduates of Bachelor of Engineering in Mechanical Engineering Program will be able to:

1. Design and develop mechanical as well as inter disciplinary components by experimental, numerical and analytical techniques

2. Apply their knowledge from field of mathematics and science fields to solve problems related to mechanical engineering.

Program Outcomes

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 solutions for complex engineering problems and design system components or processes 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.

Course Description Fluid mechanics is the branch of physics that studies fluids (liquids, gases, and plasmas) and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion. It is a branch of continuum mechanics, a subject which models matter without using the information that it is made out of atoms, that is, it models matter from a macroscopic viewpoint rather than from a microscopic viewpoint. The subject Fluid Mechanics has a wide scope and is of prime importance in several fields of engineering and science. Course Objectives

1. To give fundamental knowledge of fluid, its properties and behaviors under various fluid conditions and Introducing viscosity and show what are Newtonian and non-Newtonian fluids

2. To develop understanding about hydrostatic law, principle of buoyancy and stability of a floating body and application of mass, momentum and energy equation in fluid flow.

3. To assimilate basic laws and equations used for analysis of static and dynamic fluids. 4. To inculcate the importance of fluid flow measurement and its application in industries. 5. To determine the losses in a flow system, flow through pipes, boundary layer flow. 6. To understand dimensional analysis and theory and applications of Model Similitude.

Course Outcomes 1. To describe the mechanics of fluids at rest and in motion by observing the fluid phenomena. 2. To evaluate the kinematic properties of fluids 3. To explain Continuity Equation, Euler’s Equation, Bernoulli’s equation with its real life applications 4. To Examine energy losses in pipe transitions and sketch energy gradient lines. 5. To analyze the laminar flow characteristics through circular pipe or plates. 6. To differentiate dimensionless numbers used for various real field applications along with

dimensional analysis.

5

CO-PO MAPPING

Fluid Mechanics

Sr. No. Course Outcome (CO) 1. To describe the mechanics of fluids at rest and in motion by observing the fluid

phenomena. 2. To evaluate the kinematic properties of fluids.. 3. To explain Continuity Equation, Euler’s Equation, Bernoulli’s equation with its real life

applications 4. To Examine energy losses in pipe transitions and sketch energy gradient lines. 5. To analyze the laminar flow characteristics through circular pipe or plates. 6. To differentiate dimensionless numbers used for various real field applications.

Program Specific Outcomes

The graduates of Bachelor of Engineering in Mechanical Engineering Program will be able to:

1. Design and develop mechanical as well as inter disciplinary components by experimental, numerical and analytical techniques

2. Apply their knowledge from field of mathematics and science fields to solve problems related to mechanical engineering.

Course Outcomes

PO1

PO2

PO3

PO4

PO5

PO6

PO7

PO8

PO9

PO10

PO11

PO12

PSO

1

PSO

2

CO1 3 3 2 2 1 - - - - - - 2 2 3 CO2 3 3 2 2 1 - - - - - - 1 2 2 CO3 3 2 2 3 1 1 - - - - 1 2 2 2 CO4 2 2 2 2 - - 1 - - - - 2 2 2 CO5 3 2 2 3 - - - - - - - 1 2 1 CO6 2 2 2 2 1 - 1 - - - - 2 2 2 Mean 2.3 2.3 2 2.3 1.0 1.0 1.0 1.0 1.7 2 2

B. Tech. III Semester

Fluid Mechanics L T P/D Total Max Marks: 100 Marks 3- 0- 2 5 Final Exam: 70 Marks Sessional: 20 Marks Internals: 10 Marks. Module: 1 (8 lectures) Definition of fluid, Units and dimensions, Newton’s law of viscosity, Properties of fluids, mass, density, specific volume, specific gravity, viscosity, surface tension and capillarity, vapor pressure, compressibility and bulk modulus. Hydrostatics; fluid force on plane and curved surfaces, manometers, buoyancy, uniformly accelerated motion. Module: 2 (4 lectures) Kinematics of fluid flow: Generalized continuity equation, Irrotational motion and solution to Laplace equation. Concept of stream lines, Equipotential Lines, Flow Nets. Module: 3 (6 lectures) Dynamics of fluid flow: Control volume and control surface, application of continuity equation and momentum equation, Bernoulli’s equation and its applications. Module: 4 (4 lectures) Concept of boundary layer, boundary layer thickness, Displacement thickness, momentum thickness, energy thickness. Module: 5 (8 lectures) Laminar viscous flow through circular conduits, Couette and Poisuielle flow, Turbulent flow through pipes, Darcy Weisbach equation, friction factor for smooth and rough pipes, Moody’s diagram. Module: 6 (6 lectures) Need for dimensional analysis, methods of dimension analysis, Similitude and types of similitude, Dimensionless parameters, application of dimensionless parameters Model analysis. Module: 7 (6 lectures) Forces on immersed bodies, concepts of separation, drag force, circulation and lift force.

GATE SYLLABUS

Fluid Mechanics

Fluid Mechanics: Properties of fluids, fluid statics; Continuity, momentum, energy and corresponding equations; Potential flow, applications of momentum and energy equations; Laminar and turbulent flow; Flow in pipes, pipe networks; Concept of boundary layer and its growth.

Hydraulics: Forces on immersed bodies; Flow measurement in channels and pipes; Dimensional analysis and hydraulic similitude; Kinematics of flow,

TIME- TABLE

3rd Semester Room No. 05 Time/Day 10:00-10:50 10:50-11:40 11:40-12:30 12:30-01:20 01:20-02:00 02:00-02:50 02:50-03:40 03:40:5:20 Mon FM

L

U N C H

Tue FM Lab

Wed FM

Thur FM Lab

Fri FM

Sat

Student List

Sl. No.

Registration No.

Name

1 17102117027 DINESH KUMAR CHOUDHARY

2 18102117003 NIKHIL PRAKASH 3 18102117004 CHANDAN KUMAR 4 18102117005 SHANTANU PRABHAKAR 5 18102117006 NITESH KUMAR 6 18102117007 SANTOSH KUMAR 7 18102117008 PRINCE KUMAR 8 18102117009 BIBHANSHU CHANDRA 9 18102117010 UDAY BHANU KUMAR 10 18102117011 ANKIT KUMAR 11 18102117012 DIBYANSHU KUMAR

SHARMA 12 18102117013 ABHINAV ANAND 13 18102117014 SAUMYA 14 18102117015 MANISH KUMAR 15 18102117017 GUNJAN GUPTA 16 18102117018 JYOTI KUMARI 17 18102117019 NITESH SINGH 18 18102117021 CHANDRASHEKHAR KUMAR 19 18102117022 RAVI KUMAR 20 18102117023 VISHAL KUMAR 21 18102117024 VED PRAKASH 22 18102117025 ABHASH RANJAN 23 18102117026 ABUZAR 24 18102117027 ANKIT KUMAR 25 18102117028 OM KUMAR GUPTA 26 18102117030 KUMAR GYANESH 27 18102117031 SANDEEP KUMAR 28 18102117032 SUMAN KUMAR SAHANI 29 18102117033 HOZAIFA IQUBAL 30 18102117035 OMPRAKASH SAFI 31 18102117036 MD ASHIF ANWAR 32 18102117037 MANISH KUMAR 33 18102117038 VIKASH KUMAR 34 18102117039 KUMAR SANDEEP

35 18102117040 SHIVAM RAJ 36 18102117041 MANISH KUMAR 37 18102117042 ABHISHEK RAJ 38 18102117043 PREMSHANKAR 39 18102117044 RAJEEV KUMAR 40 18102117045 KUMAR AMAN 41 18102117046 RAMBABU KUMAR YADAV 42 18102117047 ANSHIKA RANI 43 18102117049 RAUNAK KUMAR 44 18102117051 PRASHANT KUMAR SUMAN 45 19102117901 PRAVEEN KUMAR GOND 46 19102117902 MD MUNIS PARVEZ 47 19102117903 LALIT KUMAR PANDIT 48 19102117904 MD AFZAL 49 19102117905 AWINASH KUMAR 50 19102117906 ROHIT SHARMA 51 19102117907 AMAN KUMAR 52 19102117908 MUNMUN KUMAR 53 19102117909 VIVEK KUMAR 54 19102117910 AJIT KUMAR 55 19102117911 BHARAT KUMAR 56 19102117912 ASHISH SUMAN 57 19102117913 DEEPAK KUMAR

Page 1 of 5

1. Scope and Objectives of the Course

This course is designed to understand basic laws, principles and phenomena in the area of fluid mechanics within the Civil Engineering curriculum. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion Pre-requisites 1. Basic system of units 2. Statics and dynamics 3. Fundamental concepts and laws of mechanics including equilibrium and Newton’s laws of motion 4. Differential calculus After attending this course, student should be able to do the following: 1. Define the fluid properties and differentiate types of fluids 2. Describe the concept of Surface Tension and capillarity 3. Understand Fluid hydrostatics, Center of pressure, buoyancy and floatation. 4. Understand the methods of describing fluid motion 5. Understand the dynamics of fluid flow 6. Examine the force on immersed bodies 7. Understand various dimensionless numbers and their real field applications.

2. Textbooks

TB1: ‘Bansal, R. K. (2011), “Textbook of fluid mechanics and hydraulic machine: SI units”, New Delhi, India: Laxmi Publication. TB2: ‘Rajput, R.K. (2016), “Fluid Mechanics and Hydraulic Machines”, S. Chand Publication.

3. Reference Books

RB1: White, F. M. (2008). Fluid mechanics. New Delhi: Tat McGraw Hill. RB2: Rathakrishnan, E. (2009). Fluid mechanics: an introduction. New Delhi, India: PHI Learning.

Other readings and relevant websites

S. No.

Link of Journals, Magazines, websites and Research Papers

1. http://www.informit.com/articles/article.aspx?p=2832417&seqNum=4 2. https://nptel.ac.in/courses/105103095/15 3. http://www.engineeringenotes.com/civil-engineering/notes-on-buoyancy-and-

floatation-differences-problems-and-solutions-fluid-mechanics/47027 4. https://nptel.ac.in/courses/105103095/42 5. http://vlab.amrita.edu/?sub=62&brch=176&sim=1635&cnt=1

Institute / School Name : LOK NAYAK JAY PRAKASH INSTITUTE OF TECHNOLOGY CHAPRA

Program Name B.TECH. ME Course Code ME203 Course Name FLUID MECHANICS Lecture / Tutorial (per week): 3/1 Course Credits 4.5 Course Coordinator Name PRAVIN RAI

Page 2 of 5

6. Course Plan Lecture Number

Topics Web Links for video lectures

Text Book / Reference Book / Other reading material

Page numbers of Text Book(s)

1-4 Introduction to Fluid Mechanics TB1 1-26 Physical properties of fluids,

density, viscosity, compressibility, ideal and real fluids. Surface tension and Capillarity

https://www.youtube.com/watch?v=fa0zHI6nLUo&list=PLbMVogVj5nJTZJHsH6uLCO00I-ffGyBEm https://www.youtube.com/watch?v=rr8LAljAeMs&list=PLbMVogVj5nJTZJHsH6uLCO00I-ffGyBEm&index=2 https://www.youtube.com/watch?v=eqpc_ayjjP4&list=PLbMVogVj5nJTZJHsH6uLCO00I-ffGyBEm&index=3

https://nptel.ac.in/courses/105103095/1 https://nptel.ac.in/courses/105103095/4 https://nptel.ac.in/courses/105103095/5 https://nptel.ac.in/courses/105103095/7 https://nptel.ac.in/courses/105103095/60

Tutorial - 1 5-10 Hydrostatics TB1 Pascal’s law, Absolute, Gauge,

Atmospheric and Vacuum pressure, Measurement of Pressure, Simple Manometers, Hydrostatic forces on Surfaces, Total pressure and Center of Pressure, Buoyancy and Floatation, Metacentric Height

https://www.youtube.com/watch?v=vXPtNNLEOUc&list=PLbMVogVj5nJTZJHsH6uLCO00I-ffGyBEm&index=4 https://www.youtube.com/watch?v=IM7CDFNHHDY&list=PLbMVogVj5nJTZJHsH6uLCO00I-ffGyBEm&index=5 https://www.youtube.com/watch?v=bmcuR1tpyKw&list=PLbMVogVj5nJTZJHsH6uLCO00I-ffGyBEm&index=6 https://www.youtube.com/watch?v=y1p9MfRZsh8&list=PLbMVogVj5nJTZJHsH6uLCO00I-ffGyBEm&index=7 https://www.youtube.com/watch?v=qFODl0Qt4rg&list=PLbMVogVj5nJTZJHsH6uLCO00I-ffGyBEm&index=8

https://nptel.ac.in/courses/105103095/10 https://nptel.ac.in/courses/105103095/11 https://nptel.ac.in/courses/105103095/15 https://nptel.ac.in/courses/105103095/13 https://nptel.ac.in/courses/105103095/19 https://nptel.ac.in/courses/105103095/20 https://nptel.ac.in/courses/105103095/21

35-48, 69-86, 131-144

Tutorial – 2, Assignment I

Page 3 of 5

11-19 Kinematics of fluid flow TB1 163-197

Introduction, Methods of describing fluid motion, Types of fluid flow, Continuity equation, Continuity equation in three-dimensions, velocity and acceleration, velocity potential function and stream function, Flow net, Types of motion, vortex flow equation of forced vortex flow

https://www.youtube.com/watch?v=5H0euuo1PGQ&list=PLbMVogVj5nJTZJHsH6uLCO00I-ffGyBEm&index=10 https://www.youtube.com/watch?v=zWfN21s1R7w&list=PLbMVogVj5nJTZJHsH6uLCO00I-ffGyBEm&index=11 https://www.youtube.com/watch?v=0HT0OZlGUS0&list=PLbMVogVj5nJTZJHsH6uLCO00I-ffGyBEm&index=12

https://nptel.ac.in/courses/105103095/26 https://nptel.ac.in/courses/105103095/28 https://nptel.ac.in/courses/105103095/29 https://nptel.ac.in/courses/105103095/31 https://nptel.ac.in/courses/105103095/30

Tutorial – 3, Assignment-II 20-29 Dynamics of fluid flow TB1 70-

140 Introduction, Equation of motion,

Euler’s equation of motion, Bernoulli’s equation from Euler’s equation, practical applications of Bernoulli’s equation, venturimeter, orificemeter, Pitot tube, The momentum equation, moment of momentum equation, Notches and Weirs, Discharge over rectangular and triangular notch, Advantage of triangular notch over rectangular notch.

https://www.youtube.com/watch?v=aLIpG6C3B5U&list=PLbMVogVj5nJTZJHsH6uLCO00I-ffGyBEm&index=22 https://www.youtube.com/watch?v=GvJzGIno4jw&list=PLbMVogVj5nJTZJHsH6uLCO00I-ffGyBEm&index=23 https://www.youtube.com/watch?v=GvJzGIno4jw&list=PLbMVogVj5nJTZJHsH6uLCO00I-ffGyBEm&index=23 https://www.youtube.com/watch?v=JwFmOrMjLcg&list=PLbMVogVj5nJTZJHsH6uLCO00I-ffGyBEm&index=24

https://nptel.ac.in/courses/105103095/36 https://nptel.ac.in/courses/105103095/37 https://nptel.ac.in/courses/105103095/44 https://nptel.ac.in/courses/105103095/47 https://nptel.ac.in/courses/105103095/50

259-298 355-361

Tutorial – 4, Assignment-III 30-38 Introduction to Navier Stoke’s

Equation TB1 387-

404 465-483

Introduction to viscous flow, Flow of viscous fluid through Circular pipe, Flow of viscous fluid between two parallel plates, Kinetic energy and momentum correction factors, Loss of Energy in pipes, Loss of Energy due to friction, Minor Energy losses, Pipe networks

https://www.youtube.com/watch?v=9A-9W63D_mY&list=PLbMVogVj5nJTZJHsH6uLCO00I-ffGyBEm&index=29 https://www.youtube.com/watch?v=dvbYN28PuFM&list=PLbMVogVj5nJTZJHsH6uLCO00I-

https://nptel.ac.in/courses/105103095/76 https://nptel.ac.in/courses/105103095/75

547-552

Page 4 of 5

ffGyBEm&index=30 https://www.youtube.com/watch?v=dvbYN28PuFM&list=PLbMVogVj5nJTZJHsH6uLCO00I-ffGyBEm&index=30

Tutorial – 5 , Assignment -IV 39-46 Forces on Immersed bodies and

Dimensional Analysis TB1,

Introduction to Drag and Lift, Expression for Drag and Lift, Drag on a sphere, Development of lift on an airfoil, Introduction to Dimensional and Model Analysis, Dimensional Homogeneity, Methods of Dimensional Analysis, Rayleigh’s method, Buckingham’s theorem, Model Analysis, Similitude, Types of Forces, Dimensionless numbers, Models or Similarity Laws, Classification of models.

https://www.youtube.com/watch?v=jbc15fj6hnM https://www.youtube.com/watch?v=i2a6CDd-Yko&list=PLbMVogVj5nJTZJHsH6uLCO00I-ffGyBEm&index=36 https://www.youtube.com/watch?v=8yprqtrpZP4&list=PLbMVogVj5nJTZJHsH6uLCO00I-ffGyBEm&index=37 https://www.youtube.com/watch?v=6VeCQeb7TZk

https://nptel.ac.in/courses/105103095/56 https://nptel.ac.in/courses/105103095/57 https://nptel.ac.in/courses/105103095/58 https://nptel.ac.in/courses/105103095/59

657-671 686-687 559-610

Tutorial 6 Assignment V

1. Evaluation Scheme: Component 1* Sessional Test (ST)* 20 Component 2 Assignment Evaluation 10 Component 3** End Term Examination** 70 Total 100

SYLLABUS

Topics No of lectures Weightage Introduction to Fluid Mechanics: Physical properties of fluids, density, viscosity, compressibility, ideal and real fluids. Surface tension and Capillarity

4 9%

Hydrostatics: Pascal’s law, Absolute, Gauge, Atmospheric and Vacuum pressure, Measurement of Pressure, Simple Manometers, Hydrostatic forces on Surfaces, Total pressure and Center of Pressure, Buoyancy and Floatation, Metacentric Height

6 14%

Kinematics of fluid flow: Introduction, Methods of describing fluid motion, Types of fluid flow, Continuity equation, Continuity equation in three-dimensions, velocity and acceleration, velocity potential function and stream function, Flow net, Types of motion, vortex flow equation of forced vortex flow

9 19%

Dynamics of fluid flow: Introduction, Equation of motion, Euler’s equation of motion, Bernoulli’s equation from Euler’s equation, practical applications of Bernoulli’s equation, venturimeter, orificemeter, Pitot tube, The momentum equation, moment of

10 22%

Page 5 of 5

momentum equation, Notches and Weirs, Discharge over rectangular and triangular notch, Advantage of triangular notch over rectangular notch. Introduction to Navier Stoke’s Equation: Introduction to viscous flow, Flow of viscous fluid through Circular pipe, Flow of viscous fluid between two parallel plates, Kinetic energy and momentum correction factors, Loss of Energy in pipes, Loss of Energy due to friction, Minor Energy losses, Pipe networks

9 19%

Forces on Immersed bodies and Dimensional Analysis: Introduction to Drag and Lift, Expression for Drag and Lift, Drag on a sphere, Development of lift on an airfoil, Introduction to Dimensional and Model Analysis, Dimensional Homogeneity, Methods of Dimensional Analysis, Rayleigh’s method, Buckingham’s theorem, Model Analysis, Similitude, Types of Forces, Dimensionless numbers, Models or Similarity Laws, Classification of models.

8 17%

This Document is approved by: Designation Name Signature

Course Coordinator Mr. Pravin Rai

H.O.D Mr. Jyotiraditya Kumar

Principal Dr. S.N.Sharma

Date

Evaluation and Examination Blue Print: Sessional Test 20% Internals 10% End term examination 70%

Page 1 of 2

LECTURE PLAN Topics Lecture

Number Date on which the Lecture was taken

Introduction to Fluid Mechanics Physical properties of fluids, density, viscosity 1 compressibility, ideal and real fluids 2 Surface tension and Capillarity 3 Numericals 4 Hydrostatics Pascal’s law, Absolute, Gauge, Atmospheric and Vacuum pressure, 5 Measurement of Pressure and Numericals 6 Simple Manometers, Hydrostatic forces on Surfaces, 7 Total pressure and Center of Pressure 8 Buoyancy and Floatation 9 Metacentric Height & Numericals based on Hydrostatics 10 Kinematics of fluid flow Introduction, Methods of describing fluid motion 11 Types of fluid flow 12 Continuity equation, Continuity equation in three-dimensions 13 Numericals based on Continuity Equation 14 Velocity and acceleration 15 Velocity potential function and stream function 16 Flow net and its applications 17 Types of motion 18 Free and Forced Vortex flow 19 Dynamics of fluid flow Introduction, Equation of motion 20 Euler’s equation of motion 21 Bernoulli’s equation from Euler’s equation 23 Practical applications of Bernoulli’s equation, Venturimeter 24 Introduction to orificemeter 25 Introduction to Pitot tube 26 The momentum equation, moment of momentum equation 27 Introduction to Notches and Weirs 28 Discharge over rectangular and triangular notch, Advantage of triangular notch over rectangular notch.

29

Introduction to Navier Stoke’s Equation Introduction to viscous flow 30 Flow of viscous fluid through Circular pipe 31 Flow of viscous fluid through Circular pipe Contd. 32 Flow of viscous fluid between two parallel plates 33 Kinetic energy and momentum correction factors 34 Loss of Energy in pipes 35 Loss of Energy due to friction 36 Minor Energy losses & Numericals based on energy losses. 37 Pipe networks- Hardy’s Methods 38 Forces on Immersed bodies and Dimensional Analysis

Institute / School Name : LOK NAYAK JAI PRAKASH INSTITUTE OF TECHNOLOGY, CHAPRA

Program Name B.TECH. ME Course Code ME203 Course Name FLUID MECHANICS Lecture / Tutorial (per week): 3/0 Course Credits 4.5 Course Coordinator Name PRAVIN RAI

Page 2 of 2

Introduction to Drag and Lift 39 Expression for Drag and Lift 40 Drag on a sphere 41 Development of lift on an airfoil 42 Introduction to Dimensional and Model Analysis, Dimensional Homogeneity

43

Methods of Dimensional Analysis, Rayleigh’s method 44 Buckingham’s pie-theorem, Model Analysis, Similitude 45 Types of Forces, Dimensionless numbers, Models or Similarity Laws, Classification of models.

46

Assignment-I

Fluid Mechanics

Q.1 Briefly explain the types of fluids.

Q.2 Determine the intensity of shear of an oil having viscosity=1poise. The oil is used is used for lubricating the clearance between a shaft of diameter 10cm and its journal bearing. The clearance is 1.5mm and the shaft rotates at 150 rpm

Q. 3 Two horizontal plates are placed 1.25cm apart, the space between them filled with oil of viscosity 14 poises. Calculate the shear stress in oil if upper plate is moved with a velocity of 2.5m/s.

Q.4 The velocity profile of a viscous fluid over a plate is parabolic with vertex 20cm from the plate, where the velocity is 120cm/s. Calculate the velocity gradient and shear stress at a distance of 0, 5 and 15cm from the plate, given the viscosity of fluid is 6poise.

Q.5 Calculate the dynamic viscosity of an oil, which is used for lubrication between a square plate of size 0.8m *0.8m and an inclined plane with angle of inclination 30o. The weight of the square plate is 300N and it slides down the inclined plane with a uniform velocity of 0.3m/s. The thickness of oil film is 1.5mm.

Q. 6 Find the kinematic viscosity of an oil having density 9.81kg/m3. The shear stress at a point in oil is 0.2452 N/m2 and velocity gradient at that point is 0.2 per second.

Q.7 A Newtonian fluid is filled in the clearance between a shaft and a concentric sleeve. The sleeve attains a speed of 50cm/s, when a force of 40N is applied to the sleeve parallel to the shaft. Determine the speed if a force of 200N is applied.

Q. 8 The pressure outside the droplet of water of diameter 0.04mm is 10.32 N/cm2 (atmospheric pressure). Calculate the pressure within the droplet if surface tension is given as 0.0725 N/m of water.

Q. 9 The capillary rise in the glass tube is not to exceed 0.2mm of water. Determine its minimum size, given that surface tension for water in contact with air = 0.0725 N/m.

Assignment-II Fluid Mechanics-I

1. Discuss the following cases of potential flow in brief:

a) Uniform Flow b) Source Flow c) Superimposed Flow d) Sink Flow

2. A jet of water from a 25mm diameter nozzle is directed vertically upwards. Assuming that the jet remains circular and neglecting any loss of energy, what will be the diameter at a point 4.5m above the nozzle, if the velocity with which the jet leaves the nozzle is 12m/s. (Refer Fig. 1)

3. The velocity vector in a fluid is given by V= 2x3 î – 5x2y ĵ – 4t k. Find the velocity and acceleration of a fluid particle at (1,2,3) at time t=1.

4. For the velocity potential function Φ = x2 – y2, find the velocity components at the point (4,5).

5. Water flows through a pipe AB 1.2m diameter at 5m/sec and then passes through a pipe BC 1.5m diameter. At C, the pipe branches CD is 0.8m in diameter and carries one third of the flow in AB. The flow velocity in branch CE is 3m/s. Find the volume and rate of flow in AB, the velocity in BC, velocity in CD and the diameter of CE. (Refer Fig.2)

6. For the velocity components given as u = aySinxy, v = axSinxy. Obtain an expression for the velocity potential function.

7. A fluid flow is given by v= 10x3 î – 8x3y ĵ. Find the shear strain rate and state whether the flow is rotational or irrotational.

8. An open circular cylinder of 20cm diameter and 100cm long contains water up to a height of 80cm.It is rotated about its vertical axis. Find the speed of rotation, when

a) No water spills. b) Axial depth is zero.

9. If for a two-dimensional potential flow, the velocity potential is given by Φ = 4x(3y-4), determine the velocity at the point (2,3). Determine also the value of stream function, Ψ at the point (2,3).

Figure 1 {Question 2}

Figure 2 {Question 5}

Assignment-III Fluid Mechanics

1. Water is flowing through a pipe having diameter 300mm and 200mm at the bottom and upper end respectively. The intensity of pressure at the bottom end is 24.525 N/cm2 and the pressure at the upper end is 9.81 N/cm2. Determine the difference in datum head if the rate of flow through pipe is 40 lit/s.

2. A pipeline carrying oil of specific gravity 0.87, changes in diameter from 200mm diameters at a position A to 500mm diameter at a position B which is 4 metres at a higher level. If the pressures at A and B are 9.81 N/cm2 and 5.886 N/cm2 respectively and the discharge is 200 litres/s. Determine the loss of head and direction of flow.

3. An oil of Sp. Gr. 0.8 is flowing through a venturimeter having inlet diameter 20cm and throat diameter 10 cm. The oil-mercury differential manometer shows a reading of 25 cm. Calculate the discharge of oil through the horizontal venturimeter. Take Cd = 0.98.

4. A 30cm x15 cm venturimeter is inserted in a vertical pipe carrying water, flowing in the upward direction. A differential mercury manometer connected to the inlet and throat gives a reading of 20cm. Find the discharge. Take Cd = 0.98

5. A 30cm x 15 cm venturimeter is provided in a vertical pipeline 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:

a) The discharge of oil, and b) The pressure difference between the entrance section and the throat section. Take the co-efficient

of discharge as 0.98 and specific gravity of mercury as 13.6

6. A 300mm diameter pipe carries water under a head of 20metres with a velocity of 3.5 m/s. If the axis of the pipe turns through 450, find the magnitude and direction of the resultant force at the bend.

7. In a 450 bend a rectangular air duct of 1m2 cross-sectional area is gradually reduced to 0.5 m2 area. Find the magnitude and direction of the force required to hold the duct in position if the velocity of flow at the 1 m2 section is 10m/s, and pressure is 2.943 N/cm2. Take density of air as 1.16 kg/m3.

8. Define the relative merits and demerits of venturimeter with respect to orificemeter.

9. In a 200mm diameter horizontal pipe a venturimeter of 0.5 contraction ratio has been fixed. The head of water on the venturimeter when there is no flow is 4m (gauge). Find the rate of flow for which the throat pressure will be 4 metres of water absolute. Take Cd = 0.97 and atmospheric pressure head = 10.3 m of water.

10. An orifice meter with orifice diameter 15 cm is inserted in a pipe of 30 cm diameter. The pressure gauges fitted upstream and downstream of the orifice meter give reading of 14.715 N/cm2 and 9.81 N/cm2 respectively. Find the rate of flow of water through the pipe in litres/sec. Take Cd = 0.6.

11. (a) Name the different forces present in a fluid flow. For Euler’s equation of motion, which forces are taken into consideration.

(b) What is the difference between pitot-tube and pitot-static tube?

Assignment-IV Fluid Mechanics

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

2. Calculate the pressure gradient along flow, the average velocity and the discharge for an oil of viscosity 0.02 Ns/m2 flowing between two stationary parallel plates 1m wide maintained 10mm apart. The velocity midway between the plates is 2m/s.

3. An oil of viscosity 10 poise flows between two parallel fixed plates which are kept at a distance of 50mm apart. Find the rate of flow of oil between the plates if the drop of pressure in a length of 1.2m be 0.3N/cm2. The width of the plates is 200mm.

4. A crude oil of kinematic viscosity 0.4 stoke is flowing through a pipe of diameter 300mm at the rate of 300 litres parsec. Find the head lost due to friction for a length of 50m of the pipe.

5. Calculate the discharge through a pipe of diameter 200mm when the difference of pressure head between the two ends of pipe 50m apart is 4m of water. Take the value of f=o.009 in Darcy equation.

6. Find the loss of head when a pipe of diameter 200mm is suddenly enlarged to a diameter of 400mm. The rate of flow of water through the pipe is 250lit/s.

7. A horizontal pipe of diameter 500mm is suddenly contracted to a dimeter of 250mm. The pressure intensities in the large and smaller pipe is given as 13.734 N/cm2 and 11.772 N/cm2 respectively. Find the loss of head due to contraction if Cc = 0.62. Also determine the rate of flow of water.

8. A 150mm diameter pipe reduces in diameter abruptly to 100mm diameter. If the pipe carries water at 30 litres per second, calculate the pressure loss across the contraction. Take the Cc= 0.60.

9. Water is flowing through a horizontal pipe of diameter 200mm at a velocity of 3m/s. A circular solid plate of diameter 150mm is placed in the pipe to obstruct the flow. Find the loss of head due to obstruction in the pipe, if Cc=0.62

Assignment-V Fluid Mechanics-I

1. The time period (t) of a pendulum depends upon the length (L) of the pendulum and acceleration due to gravity (g). Derive an expression for the time period.

2. Find the expression for the power P, developed by a pump when P depends upon the head, H and the discharge Q and specific weight, w of the fluid.

3. The efficiency ƞ of a fan depends on the density ρ, the dynamic viscosity µ of the fluid, the angular velocity ɷ, diameter D of the rotor and the discharge Q. Express ƞ in terms of dimensionless parameters.

4. The pressure difference Δp 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. Using Buckingham’s ᴨ-theorem, obtain an expression for Δp.

5. What are the advantages of dimensional and model analysis?

6. A ship model of scale 1/50 is towed through sea water at a speed of 1m/s. A force of 2N is required to tow the model. Determine the speed of ship and the propulsive force on the ship, if prototype is subjected to wave resistance only.

7. Experiments were conducted in a wind tunnel with a wind speed of 50 km/h on a flat plate of size 2 m long and 1 m wide. The density of air is 1.15 kg/m3. The co-efficient of lift and drag are 0.75 and 0.15 respectively. Determine: (i) the lift force (ii) the drag force (iii) the resultant force (iv) direction of resultant force and (v) power exerted by air on the plate.

8. A circular disc 3 m in diameter is held normal to a 26.4 m/s wind of density 0.0012 gm/cc. What force is required to hold it at rest? Assume co-efficient of drag of disc = 1.1.

9. A man weighing 90 kgf descend to the ground from an aeroplane with the help of a parachute against the resistance of air. The velocity with which the parachute, which is hemispherical in shape, comes down is 20 m/s. Find the diameter of the parachute. Assume CD = 0.5 and density of air = 1.25 kg/m3.

10. A man descends to the ground from an aeroplane with the help of a parachute which is hemispherical having a diameter of 4 m against the resistance of air with a uniform velocity of 25 m/s. Find the weight of the man if the weight of parachute is 9.81 N. Take CD =0.6 and density of air = 1.25 kg/m3.

11. An airfoil of chord length 2 m and of span 15 m has an angle of attach as 60. The airfoil is moving with a velocity of 80 m/s in air and whose density is 1.25kg/cubic m. Find the weight of the airfoil and the power required to drive it. Take CD = 0.03 and CL = 0.5 respectively.

Tutorials 1

1. One lire of crude oil weighs 9.6N. Calculate its specific weight, density and specific gravity.

2. A plate 0.025mm distant from a fixed plate, moves at 50cm/s and requires a force of 1.471N/mm2 to maintain this speed. Determine the fluid viscosity between the plates in the poise.

3. Determine the intensity of shear of an oil having viscosity =1.2 poise and is used for lubrication in the clearance between a 10cm diameter shaft and its journal bearing. The clearance is 1mm and shaft rotates at 200rpm.

4. An oil of viscosity 5poise is used for lubrication between a shaft and sleeve. The diameter of shaft is 0.5m and it rotates at 200rpm. Calculate the power lost in the oil for a sleeve length of 100mm. The thickness of Oil film is 1mm.

5. The pressure of a liquid is increased from 60N/cm2 to 100 N/cm2 and volume decreases by 0.2%. Determine he bulk modulus of elasticity.

6. Determine the bulk modulus of elasticity of a fluid which is compressed in a cylinder from a volume of 0.009 m3 at 70N/cm2 pressure to a volume of 0.0085 m3 at 270N/cm2 pressure.

7. Find the surface tension in a soap bubble of 30mm diameter when the inside pressure is 1.962 N/m2 above atmosphere.

8. The surface tension of water in contact with air at 20’c is given as 0.0716 N/m. The pressure inside a droplet of water is to be 0.0147 N/cm2 greater than the outside pressure, calculate the diameter of the droplet of water.

9. Calculate the capillary rise in a glass tube of 3mm diameter when immersed vertically in (a) water, and (b) Mercury. Take surface tension for mercury and water as 0.0725N/m and 0.52N/m respectively in contact with air. Specific gravity for mercury is given as 13.6.

10. A square plate of size 1m x 1m and weighing 350N slides down an inclined plane with a uniform velocity of 1.5m/s. The inclined plane is laid on a slope of 5vertical to 12 Horizontal and has an oil film of 1mm thickness. Calculate the dynamic viscosity of oil

Tutorials 2

1. An oil of specific gravity 08 is contained in a vessel. At a point the height of oil is 20m. Find the corresponding height of water at that point.

2. An open tank contains water up to a depth of 1.5m and above it an oil of specific gravity 0.8 for a depth of 2m. Find the pressure intensity i. at the interface of the two liquids and ii. At the bottom of the tank.

3. Determine the gauge and absolute pressure at a point which is 2m below the free surface of water. Take the atmospheric pressure as 10.1043 N/cm2.

4. A pipe contains an oil of specific gravity 0.8. A differential manometer connected at the two points A and B of the pipe shows a difference in mercury level as 20cm. Find the difference of pressure at the two points.

5. An inverted differential manometer containing an oil of specific gravity 0.9 is connected to find the difference of pressures at two points of a pipe containing water. If the manometer reading is 40cm, find the difference of pressures.

6. What are the gauge pressure and absolute pressure in N/m2 at a point 4m below the free surface of a liquid of specific gravity 1.2, if the atmospheric pressure is equivalent to 750m of Mercury.

7. Determine the total pressure on a circular plate of diameter 1.5m which is placed vertically in water in such a way that center of plate is 2m below the free surface of water. Find the position of center of pressure also.

8. A rectangular tank 4m long, 1.5m wide contains water up to a height of 2m. Calculate the force due to water pressure on the base of the tank. Find the depth pf center of pressure from the free surface.

9. A rectangular pontoon is 4m long, 3m wide and 1.40m high. The depth of immersion of the pontoon is 1m in sea-water. If the center of gravity is 0.70m above the bottom of the pontoon, determine the metacentric height. Take the density of sea water as 1030 kg/m3.

10. A solid cylinder of diameter 5m has a height 5m. Find the metacentric 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.

Tutorials 3

1. A 40 cm diameter pipe, conveying water, branches into two pipes of diameters 30cm and 20cm respectively. If the average velocity in the 40cm diameter pipe is 3m/s. Find the discharge in this pipe. Also determine the velocity in 20cm pipe if the average velocity is 2m/s in 30cm diameter pipe.

2. Find the convective acceleration at the middle of a pipe which converges uniformly from 0.6m diameter to 0.3m diameter over 3m length. The rate of flow is 40lit/s. If the rate of flow changes uniformly from 40lit/s to 80 lit/s in 40 seconds. Find the total acceleration at the middle of the pipe at 20th second.

3. A stream function is given by ψ = 2x-5y. Calculate the velocity components and also magnitude and direction of the resultant velocity at any point.

4. The stream function for a two-dimensional flow is given by ψ=8xy, calculate the velocity at the point p(4,5). Find the velocity potential function ϕ.

5. An open circular cylinder of 20cm diameter and 100cm long contains water up to a height of 80cm. It is rotated about its vertical axis. Find the speed of rotation when

i. no water depth, ii axial depth is zero

6. A cylindrical vessel 15cm in diameter and 40cm long is completely filled with water. The vessel is open at the top. Find the quantity of water left in the vessel, when it is rotated about its vertical axis with a speed of 300rpm.

7. A closed cylindrical vessel of diameter 15cm and length 100 cm contains water up to a height of 80cm. The vessel is rotated at a speed of 500rpm about its vertical axis. Find the height of paraboloid formed.

8. State if the flow represented by u=3x+4y and v=2x-3y is rotational or irrotational.

9.Check if ϕ=x2 – y2 +y represents the velocity potential for 2-dimensioal irrotational flow. If it does, then determine the stream function φ.

10. Define two-dimensional stream function and velocity potential. Show that the following stream function ψ=6x-4y+7xy+9 represents an irrotational flow. Find its velocity potential.

Tutorials 4

1. Water is flowing through a pipe of 100mm diameter under a pressure of 19.62 N/cm2 (gauge) and with mean velocity of 3m/s. Find the total head of the water at a cross section, which is 8m above the datum line.

2. A pipe, through which water is flowing is having diameters 40 cm and 20cm at the cross-sections 1 and 2 respectively. The velocity of water at section 1 is given 5m/sec. Find the velocity head at the sections 1 and 2 and also the rate of discharge.

3. Water is flowing through a pipe having diameters 30cm and 15cm at the bottom and upper send respectively. The intensity of pressure at the bottom end is 29.43 N/cm2 and the pressure at the upper end is 14.715 N/cm2. Determine the difference in datum in datum head if the rate of flow through pipe is 50lit/s.

4. A horizontal venturimeter with inlet and throat diameters 30cm and 15cm respectively is used to measure the flow of water. The reading of differential manometer connected to inlet and throat is 10cm of mercury. Determine the rate of flow. Take Cd =0.98

5. A 30cmx 15cm venturimeter is inserted in a vertical pipe carrying water, flowing in the upward direction. A differential mercury manometer connected to the inlet and throat gives a reading of 30cm. Find the discharge. Take Cd =0.98

6. An orifice meter with orifice diameter 15cm is inserted in a pipe of 30cm diameter. The pressure gauges fitted upstream and downstream of the orifice meter gives readings of 14.715 N/cm2 and 9.81 N/cm2 respectively. Find the rate of flow of water through the pipe in lit/s

7. The pressure difference measured by the two tappings of a pitot-static tube, one tapping pointing upstream and other perpendicular to the flow, placed in the center of a pipe line of diameter 40cm is 10cm of water. The mean velocity in the pipe is 0.75 times the central velocity. Find the discharge through the pipe. Take co-efficient of pitot-tube as 0.98.

8. A submarine moves horizontally in sea and has its axis 20m below the surface of water. A pitot-static tube placed in front of submarine and along its axis, is connected to the two points of a U-tube containing mercury. The difference of Mercury level is found to be 20cm. Find the speed of submarine. Take specific gravity of mercury and sea water as 13.6 and 1.026 respectively.

9. A 45o reducing bend is connected in a pipe line, the diameters at the inlet and outlet of the bend being 40cm and 20cm respectively. Find the force exerted by water on the bend if the intensity of pressure at inlet of bend is 21.58 N/cm2. The rate of flow of water is 500lit/s.

10. The discharge of water through a pipe of diameter 40cm is 400lit/s. If the pipe is bend by 135 degree, find the magnitude and direction of the resultant force on the bend. The pressure of flowing water is 29.43N/cm2.

11. Find the discharge of water flowing through a pipe 20cm diameter placed in an inclined position, where a venturimeter is inserted, having a throat diameter of 10cm. The difference of pressure between the main and throat by a liquid of specific gravity 0.4 in an inverted U-tube, which gives a reading of 30cm. The loss of head between the main and throat is 0.2 times the kinetic head of pipe

Tutorials 5

1. Find the discharge of water flowing over rectangular notch of 3m length when the constant head of water over the notch is 40cm. Take Cd = 0.6

2. Find the discharge over a triangular notch of angle 60 degree when the head over the triangular notch is 0.20m. Take Cd = 0.6

3. A right-angled V-Notch is used for measuring a discharge of 30lit/s. An error of 2mm was made in measuring the head over the notch. Calculate the percentage error in the discharge. Take Cd = 0.62

4. A viscous flow is taking place in a pipe of diameter 100mm. The maximum velocity is 2m/s. Find the mean velocity and the radius at which occurs. Also calculate the velocity at 30mm from the wall of the pipe.

5. A fluid of viscosity 0.5 Poise and specific gravity 1.20 is flowing through a circular pipe of diameter 100mm. The maximum shear stress at the pipe wall is given as 147.15 N/m2, find (a) the pressure gradient (b) average velocity (c) The Reynolds number of flow.

6. Water is flowing between two large parallel plates which are 2mm apart. Determine (a) maximum velocity (b) the pressure drop per unit length and (c) the shear stress at walls of the plate if the average velocity is 0.4m/s. Take viscosity of water as 0.01 poise.

7. There is a horizontal crack 50mm wide and 3mm deep in a wall of thickness 150mm. Water leaks through the crack. Find the rate of leakage of water through the crack if the difference of pressure between the two ends of the crack is 245.25 N/m2. Take the viscosity of water as 0.01 poise.

8. Water is flowing through a 150mm diameter pipe with a co-efficient of friction, f=0.05. The shear stress at a point 40mm from the pipe wall is 0.01962 N/cm2. Calculate the shear stress at the pipe wall.

9. Find the diameter of a pipe of length 2500m when the rate of flow of water through pipe is 0.25 m3/s and head loss due to friction is 5m. Take C=50 in Chezy’s formula.

10. Determine the rate of flow of water through a pipe of diameter 10cm and length 60cm when one end of the pipe is connected to a tank and other end of the pipe is open to the atmosphere. The height of water in the tank from the center of the pipe is 5cm. Pipe is given as horizontal and value of f=0.01. Consider minor losses.

11. A syphon of diameter 150mm connects two reservoirs having a difference in elevation of 15m. The length of the syphon is 400m and summit is 4m above the water level in the upper reservoir. The length of the pipe from the upper reservoir to the summit is 80m. Determine the discharge through the syphon and also pressure at the summit. Neglect minor losses. Take f=0.05

12. Three pipes of length 800m, 600m, and 300m and of diameters 400mm, 300mm, and 200mm respectively are connected in series. The ends of the compound pipe is connected to two tanks, whose waster surface levels are maintained at a difference of 15m. Determine the rate of flow of water through the pipes if f=0.05. What will be diameter of a single pipe of length 1700m and f=0.05, which replaces the three pipes?

13. Two pipes of length 2500m each and diameters 80cm and 60cm respectively, are connected in parallel. The f=0.006. The total flow is equal to 250lit/s. Find the rate of flow in each pipe.

Tutorials 6

1. The variables controlling the motion of floating vessel through water are the drag force F, the speed V, the length L, the density ρ, and dynamic viscosity µ of water and acceleration due to gravity g. Derive an expression for F by dimensional analysis.

2. A pipe of diameter 1.8m is required to transport an oil of specific gravity 0.8 and viscosity 0.04poise at the rate of 4 m3/s. Tests were conducted on a 20cm diameter pipe using water at 20’c. Find the velocity and rate of flow in the model. Viscosity of water at 20’c = 0.01 poise.

3. In 1:30 model of a spillway, the velocity and discharge are 1.5m/s and 2m3/s. Find the corresponding velocity and discharge in the prototype.

4. A 1:20 model of a flying boat is towed through waster. The prototype is moving in sea water of density 1024kg/m3 at a velocity of 15m/s. Find the corresponding speed of the model. Also determine the resistance due to waves in model, if the resistance due to waves of prototype is 500N.

5. The drag force exerted by a flowing fluid on a solid body depends upon the length of the body, L, velocity of flow V, density of fluid ρ and viscosity µ. Find the expression for drag force using Buckingham’s theorem

6. The discharge through an orifice depends on the diameter D of the orifice, head H over the orifice, density ρ of liquid, viscosity µ of the liquid and acceleration g due to gravity. Using dimensional analysis, find an expression for the discharge. Hence find the dimensionless parameters on which the discharge co-efficient of an orifice meter depend.

7. Find the drag force difference on a flat plate of size 1.5m x 1.5 m when the plate is moving at a speed of 5m/s normal to its plate first in water and second in air of density 1.24kg/m3. Co-efficient of drag is given as 1.10

8. A flat plate 2m x 2m moves at 40km/hr in stationary air of density 1.25kg/m3. If the coefficient of drag and lift are 0.2 and 0.8 respectively. Find (i) the lift force (ii) the drag force (iii) the resultant force and (iv) the power required to keep the plate in motion

Department of Civil Engineering Mid-Term Examination

Subject: Fluid Mechanics Session: 2018-19

Time: 2hrs Max. Marks: 20 Marks S. No. Marks CO’s

1 a. An ideal fluid I. Has no viscosity

II. Satisfies the relation PV=RT III. Obeys the Newton’s law of viscosity IV. is both incompressible and non-vsicous

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b. The continuity equation represents the conservation of i. Mas

ii. Momentum iii. Energy iv. Vorticity

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c. The resultant hydrostatic force acts through a point is known as

i. Center of gravity ii. Center of buoyancy iii. Center of pressure iv. None of the above

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d The stream line is a line i. Which is along the path of particle

ii. Which is always parallel to the main direction of flow

iii. Across which there is no flow iv. On which tangent drawn at any point gives the

direction of the velocity

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e Poise is the unit of i. Mass density

ii. Kinematic viscosity iii. Viscosity iv. Velocity gradient

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2. Derive the continuity equation in 3-dimensions. Also state the continuity equation in case of incompressible and steady flow.

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OR State Bernoulli’s theorem for steady flow of an

incompressible fluid. Derive an expression for Bernoulli’s equation from first principle and state the assumption made for such a derivation.

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3 If for a two-dimensional potential flow, the velocity potential is given by φ= x (2y-1). Determine the velocity at the point P (4,5). Determine also the value of stream

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function ϕ at the Point P. OR

𝑢 = 𝑦3

3 + 2𝑥− 𝑥2𝑦,𝑣 = 𝑥𝑦2 − 2𝑦−𝑥3

3

The velocity component in a two-dimensional flow are

Show that these components represents a possible case of an irrational flow.

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4. i An open circular cylinder of 15cm diameter and 100cm long contains water up to a height of 80cm. Find the maximum speed at which the cylinder is to be rotated about its vertical axis so that no water spills.

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ii. Show that equipotential lines and stream lines are orthogonal to each other.

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iii. Name the various forces acting on fluid element 1 CO2 iv. Water is flowing through a pipe having diameter 300mm

and 200mm at the bottom and upper end respectively. The intensity of pressure at the bottom end is 24.525 N/cm2 and the pressure at the upper end is 9.81 N/cm2. Determine the difference in datum head if the rate of flow through the pipes is 40 lit/s.

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