Prof. K.L. KUMARPh.D. (London), D.I.C., M.E. (Roorkee), B.E. (Delhi)

F.I.E. (India), M.I.S.T.E., M.S.F.M.F.P., M.I.S.T.A.M., M.A.S.E.E. (USA), I.M.A.I.A.E.T.Professor, Faculty of Engineering and Technology,

University of Botswana, GaboroneFormerly UNESCO Expert in Technical Education, Middle East

Professor & Head, Educational Technology and Coordinator, QIPProfessor & Head, Department of Applied Mechanics,

INDIAN INSTITUTE OF TECHNOLOGY, NEW DELHI

EURASIA PUBLISHING HOUSE (P) LTD.RAM NAGAR, NEW DELHI-110 055

Engineering FLUID

MECHANICSFor Mechanical, Civil, Electrical, Chemical, Aeronautical

and Other Engineering and Design Students

In SI Units

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© 1976, Copyright ReservedAll rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the Publishers.thout the written permisFirst Edition 1976 Subsequent Editions and Reprints1980, 84, 88, 90, 92, 95, 97, 98, 99, 2000, 2002, 2003,2004, 2006, 2007, 2008

Eighth Revised Multicolour Edition 2009; Reprints 2012, 2013; Reprint 2014

ISBN : 978-81-219-0100-6 Code : 4010B 020

printed in india

By Rajendra Ravindra Printers Pvt. Ltd., 7361, Ram Nagar, New Delhi -110 055 and published by Eurasia Publishing House (P) Ltd., 7361, Ram Nagar, New Delhi -110 055.

Sole Distributors :

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wrote the first edition of the book in love for the subject of fluid mechanics; I have revised and brought the multicolour edition as a mark of affection for the students and younger staff members !

With the passage of time since its first edition in 1976, my fascination for the subject of fluid mechanics has soared to new heights, perhaps with my own involvement with some new designs in the world full of new applications including bio-fluid mechanics, heart lung machines for heart transplants and prediction models of natural calamities such as hurricanes, tornadoes, wind storms and tsunamis!

Ever since the genius of Leonardo da Vinci drew the above concept drawing and our knowledge of fluid mechanics has realized his vision by way of aircraft, gliders, helicopters and other flying machines and a variety of fluid machines including pumps, compressors and turbines have become a reality in everyday life, the subject of fluid mechanics has become a core subject in all engineering disciplines.

I thank the Management of S. Chand & Company Ltd., specially Mr. Navin Joshi, Vice-President (Publishing) and Mr. Shishir Bhatnagar, Manager (Editorial and Pre-press) for encouraging in every way to produce the book. Thanks are also due to Mr. Rupesh Gupta, Subject Editor for his editorial contribution and Mr. Dhan Singh Karki for designing and layouting of this book.

I am pleased to dedicate the new edition to my past students who helped me learn the subject and to extend it to the present and future students and teachers in fluid mechanics all over the world!

(Kris Kumar)Formerly of IIT Delhi; Currently, Visiting Professor, IIT Mumbai and New DelhiOn Sabbatical Leave from the University of Botswana kumarkl@gmail.com and kumarkl@mopipi.ub.bw

Preface to the Eighth Revised Multicolour Edition

I

Anything new ?

Anything special ?

Does it cover our syllabus ?

Solves numerical examples ?

Answers to the unsolved problems ?

The author has tried his best to place a positive and capital ‘YES’ to each of the above questions posed by a student of engineering in Mechanical, Civil, Electrical, Chemical or Aeronautical branch belonging to (a) a progressive engineering college in India or abroad, (b) an Indian Institute of Technology or (c) A.M.I.E. Section B (New Scheme), A.M.Ae.S.I. Section A (New Scheme) or any other engineering college in Asia, Africa or Europe. How has the author achieved this ?

The author has the experience of teaching Fluid Mechanics and allied subjects at the University of Roorkee, Imperial College of Science and Technology, London University and at the Indian Institute of Technology, Delhi. Through experience, contacts or otherwise, the syllabi of a number of universities were collected. This included the universities in India and abroad. These were examined in the light of the recommendations made by the Curriculum Development Cells set up by the Government of India. The data collection step was followed by data analysis. The largest common factor was determined, mean syllabus formulated and stretched to allow 10 to 20% overlap for any institution. What has thus emerged is indeed a series of fundamental topics on flow of paramount importance to all engineering students.

Realising that engineers and designers are more concerned with the applications than with theory, the author has woven the subject-matter with an adequate number of practical applications in engineering and a number of solved numerical examples. Unsolved problems of objective, brainstorming and numerical nature have been appended and answers to most of them have been given.

The authors acknowledges the general help received from his colleagues and friends notable among who are Professor Shankar Lal, Professor R.C. Malhotra, Professor Subhash Chander, Professor D.S. Kumar, Professor V. Seshadri, Miss Neelam Arora and Miss Sureshta Arora. The author wishes to express his gratitude to the National Book Trust of India for the generous subsidy in the publication of the text. The publishers M/s Eurasia Publishing House and in particular Shri R.C. Kumar and Shri Ravi Gupta have taken keen interest in the publication.

Acknowledgements would be incomplete without a word of appreciation for my family who have put up with my midnight lamps and general restlessness. My parents, my wife and little daughters provided an ideal bookwriting atmosphere at home throughout this venture. The students whom I have taught at home and abroad and for whose sake I have learnt the subject over the years are the contributors in absentia. My effort would be rewarded if the students and teachers of engineering accept this text and send their comments for further improvements.

Prof. K.L. Kumar, I.I.T. Delhi(kumarkl@gmail.com)

Preface to the First Edition - 1976

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Acknowledgement to Engineering Institutions

The author is grateful to the authorities in the following Institutions andUniversities, who have made available their syllabi and whose faculty members

have interacted in the preparation of the revised manuscript:

Indian Institutes of Technology :(Delhi, Mumbai, Kanpur, Kharagpur, Roorkee, Guwahati and Chennai)

National Institutes of Technology:(Agartala, Allahabad, Bhopal, Calicut, Durgapur, Goa, Hamirpur, Jalandhar, Jaipur, Jammu, Jamshedpur, Kurukshetra, Nagpur, Patna, Raipur, Rourkela, Silchar, Srinagar, Surat, Surathkal, Trichy, Warangal)

Indian Institute of Science, Bangalore; Jawaharlal Nehru Technological University, Hyderabad; Uttar Pradesh Technical University; Punjab Technical University, Jalandhar; Uttarakhand Technical University, Dehradun; Visveswariah Technological University, Bangalore; Vivekanand Technical University, Bhillai;

Birla Institute of Technology and Science : Pilani and Ranchi; College of Engineering, Anna University, Chennai; Dayalbagh Engineering Institute, Agra; Delhi College of Engineering, Delhi; Engineering Colleges of Bihar; Engineering Colleges of Pune; Engineering Colleges, Karnataka; Engineering Colleges, Nagpur; Faculty of Engineering and Technology, Jadavpur, Kolkata; Government Engineering College, Ujjain; Guindy Engineering College, Chennai; Hercourt Butler Technological Institute, Kanpur; Institute of Technology, BHU, Varanasi; Jamia Milia Islamia University, Jamia Nagar, New Delhi; Jodhpur University, Jodhpur; Karnataka University, Dharwar; Kerala University, Trivandrum; M.S. University of Baroda, Vadodra; Madhav Inst. of Sc. and Technology, Gwalior; Netaji Subhas Institute of Technology, Delhi; North Eastern Regional Institute of Science and Technology, Itanagar; Osmania University, Hyderabad; PSG College of Technology, Coimbatore; Punjab Engineering College, Chandigarh; SV Univ. College of Engineering, Tirupati; Thapar Institute of Engg. and Technology, Patiala; Tripura Engineering Colleges, Tripura; Ujjain Engineering Colleges; Vellore Institute of Technology, Vellore; Victoria Jubilee Technical Institute, Mumbai; Z.H. College of Engg. and Technology, AMU, Aligarh.

Institutions Abroad :Arya Mehar University of Technology, Tehran, Iran; Asian Institute of Technology, Bangkok, Thailand; Foundation of Technical Institute, Iraq; Imperial College of Science and Technology, London., U.K.; London University, London, England; Massachusetts Institute of Technology, Boston, U.S.A.; Mehran University of Engineering and Technology, Nawabshah, Pakistan; Thangal Kunju Musaliar College of Engineering , Quilon; University of Asmara, Eritea; Azarabadegan, Tabriz, Iran; Baghdad, Iraq; Basrah, Iraq; Birmingham, England; Botswana, Gaborone, Botswana; Cairo, Egypt; Dar Es Salaam, Tanzania; Garyounis, Benghazi, Libya; Hong Kong; Ife-Ife, Nigeria; Kuwait; Mousl, Iraq; Riyadh, Saudi Arabia; Singapore; Colombo/Katubedda, Sri Lanka and University of Technology, Baghdad, Iraq.

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Contents LEARNING OBJECTIVES IN ENGINEERING FLUID MECHANICS 1 – 2

0. THE WORLD OF FLUID MECHANICS : WHAT, WHY AND HOW ? 3 – 12

1. INTRODUCTORY CONCEPTS 13 – 50

1.1 Introduction: Fluid and Non-Fluids 13 1.2 Liquid, Gas and Vapour 14 1.3 Continuum 15 1.4 Co-ordinate Systems 15 1.5 Fluid Mechanics 16 1.6 System and Fluid Particles 16 1.7 Control Volume 17 1.8 Force and Moment 17 1.9 Stress at a Point 18 1.10 Rate of Strain 20 1.11 Properties of Fluids 20 1.11.1 Density ρ : 20 1.11.2 Pressure p : 21 1.11.3 Other Thermodynamic Variables; 22 1.11.4 Newton’s Law of Viscosity; 22 1.11.5 Viscosity; 23 1.11.6 Water as a Reference Fluid; 26 1.11.7 Compressibility; 32 1.11.8 Surface Tension σ: 34 1.11.9 Capillarity, Bubbles and Liquid-Jets; 35 1.11.10 Vapour Pressure. 38 1.12 The Atmosphere 39 1.13 Classification of Fluids and Regimes of Flow 40 Supplementary Revision Examples 43 Item Bank : Objective Items with Answers 48 Question Bank : Tutorial Problems with Answers 49

2. FLUID STATICS 51 – 143

2.1 The State of Rest; Pascal’s Law 51 2.2 The Hydrostatic Law 53 2.3 Hydrostatic Force on a Submerged Plane Surface 56 2.4 Location of the Hydrostatic Force 60 2.5 Force on a Submerged Curved Surface 66 2.6 Piezometric Head 73 2.7 Single-tube Manometers 74 2.8 U-Tube Manometers 75 2.9 Differential Manometers 78 2.10 Buoyancy 86

2.11 Determination of the Metacentric Height 90 2.12 Oscillation of a Floating Body : Time Period 91 Experiment: Metacentric Height of a Floating Body 93 2.13 Liquid in a Container Subjected to an Acceleration 99 2.14 Liquid in a Container Subjected to a Constant Rotation 106 Supplementary Revision Examples 114 Item Bank : Objective Items with Answers 133 Question Bank : Tutorial Problems with Answers 135

3. FLUID KINEMATICS 144 – 197

3.1 Description of Fluid Flow 144 3.2 Dimensions of Flow 145 3.3 Steady Flow and Uniform Flow 146 3.4 Acceleration in Fluid Flow 147 3.5 Streamlines, Pathlines and Streaklines 149 3.6 Existence of Flow 152 3.7 Continuity Equation : Differential Form 152 3.8 Stream Function for Two-Dimensional Incompressible Flow 159 3.9 Continuity Equation : Integral Form 163 3.10 Average Velocity 166 3.11 Kinematics of a Fluid Element 167 3.12 Irrotational Flow 169 3.13 Flownets 171 3.14 Circulation in a Flow 182 3.15 Flow Patterns for Different References 185 Supplementary Revision Examples 188 Item Bank : Objective Items with Answers 193 Question Bank : Tutorial Problems with Answers 195

4. FLUID DYNAMICS 198 – 254

4.1 Statement of Laws for a System and Transport Theorem 198 4.2 Euler’s Equation of Motion 200 4.3 Bernoulli Equation : Derivation from the Euler’s Equation 201 4.4 Flow through a Confined Passage 203 4.5 Flow through Orifices and Mouthpieces 207 Experiment: Flow through a Converging - Diverging Duct 208 Experiment: Flow through Orifices and Nozzles 212 4.6 Euler’s Equation and Bernoulli Equation in a Streamwise Direction 217 4.7 Navier-Stokes Equation of Motion 219 4.8 Integral Momentum Equation 220 4.9 Forces on Confinements 220 4.10 Force on a Rectangular Sluice Gate 225 Experiment: Flow under a Sluice Gate 227 4.11 Impact of a Jet of Fluid on a Vane 228 Experiment: Impact of a Jet on Vanes 230 4.12 Aircraft, Jet Engines and Propeller Action 234 4.13 Angular Momentum Equation 240

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4.14 Energy Equation : Steady Flow Energy Equation 240 4.15 Bernoulli Equation : Derivation from the Energy Equation 241 4.16 Reflection on Bernoulli Equation 241 4.17 Tips for Choosing an Appropriate Control Volume 242 4.18 Correction Factors for Non-Uniform Flows 243 Supplementary Revision Examples 246 Item Bank : Objective Items with Answers 249 Question Bank : Tutorial Problems with Answers 250

5. FLOW MEASUREMENT 255 – 294

5.1 Introduction 255 5.2 Measurement of Static, Stagnation and Dynamic Pressures and Velocity 255 5.3 Measurement of Discharge through a Pipe by a Venturimeter, a Flow Nozzle and an Orificemeter. 259 Experiment: Study of Flow Rate Measuring Devices 267 5.4 Measurement of Discharge by a Weir, a Notch or a Venturi-Flume 268 5.5 Flow through a Rectangular Notch 270 5.6 Flow through a Triangular Notch 271 Experiment: Flow over a Notch or a Weir 273 5.7 Hot Wire Anemometry 279 5.8 LASER Anemometry 281 5.9 Flow Visualisation Techniques 281 Experiment: Flow Visualisation 284 Supplementary Revision Examples 285 Item Bank : Objective Items with Answers 289 Question Bank : Tutorial Problems with Answers 290

6. IDEAL FLUID FLOW 295 – 317

6.1 Introduction 295 6.2 Importance of Ideal Fluid Flow 296 6.3 The Uniform Flow 296 6.4 The Source Flow 297 6.5 The Sink Flow 298 6.6 The Free-Vortex Flow 299 6.7 Superimposed Flow Patterns 300 6.8 The Source and Sink Pair 300 6.9 The Doublet 301 6.10 A Plane Source in a Uniform Flow 302 6.11 A Source and Sink Pair in a Uniform Flow 307 6.12 A Doublet in a Uniform Flow 307 6.13 A Doublet and Free Vortex in a Uniform Flow 310 6.14 Vortex-and-Sink Flow 313 6.15 Method of Images 314 Item Bank : Objective Items with Answers 315 Question Bank: Tutorial Problems with Answers 316

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7. LAMINAR FLOW 318 – 351

7.1 Laminar and Turbulent Flows 318 Experiment: Transition from Laminar to Turbulent Flow 319 7.2 Laminar Flow through a Round Pipe 321 Experiment: Development of Flow 327 7.3 Laminar Flow through an Annulus 329 7.4 Laminar Flow between Parallel Plates 330 7.5 Laminar Flow between Co-axial Rotating Cylinders 335 7.6 Measurement of Viscosity : 338 Capillary Tube Viscometer, 339 Co-axial Cylinder Viscometer, 340 Falling-Spheres Viscometer; 342 Efflux Viscometer. 344 Supplementary Revision Examples 345 Item Bank : Objective Items with Answers 347 Question Bank : Tutorial Problems with answers 349

8. BOUNDARY LAYER FLOW 352 – 380

8.1 Introduction 352 8.2 Development of Boundary Layer 353 – Over a Flat Plate 354 – Within a Pipe 354 8.3 Estimates of Boundary Layer Region 357 8.4 Boundary Layer Equations 360 8.5 Drag on a Flat Plate 361 8.6 Nature of Turbulence 366 8.7 Smooth and Rough Surfaces 367 8.8 Boundary Layer Separation 368 8.9 Control of Separation 370 8.10 Mechanism of Transition 372 Supplementary Revision Examples 373 Item Bank : Objective Items with Answers 377 Question Bank : Tutorial Problems with Answers 378

9. FLOW AROUND IMMERSED BODIES 381 – 416

9.1 Introduction 381 9.2 Lift and Drag 381 9.3 Classification of Drag 383 9.4 Streamlined and Bluff Bodies 384 9.5 Flow around a Circular Cylinder 386 Experiment: Flow around a Circular Cylinder 392 9.6 Flow around an Aerofoil 397 9.7 Flow around Axisymmetric and Three-Dimensional Bodies 401 9.8 Forces on Immersed Bodies : Integral Momentum Equation 403

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9.9 Terminal Velocity of Body 407 Supplementary Revision Examples 410 Item Bank : Objective Items with Answers 413 Question Bank : Tutorial Problems with Answers 415

10. FLOW THROUGH PIPES 417 – 460

10.1 Introduction 417 10.2 Friction Loss in Pipe Flow : Darcy-Weisbach Formula 418 Experiment: Fully Developed Flow through Pipes 420 10.3 Minor Losses in Pipe Flow 421 Experiment: Head, Loss in a Pipe Transition 426 10.4 Energy Line and Hydraulic Gradient Line 433 10.5 Power Transmission through Pipes 435 10.6 Pipes in Series and in Parallels 438 Supplementary Revision Examples 448 Item Bank : Objective Items with Answers 457 Question Bank : Tutorial Problems with Answers 458

11. FLOW THROUGH OPEN CHANNELS 461 – 482

11.1 Uniform Flow : Chezy Equation 461 11.2 Specific Energy and Momentum Relations 469 11.3 Hydraulic Jump 472 Experiment: Study of Hydraulic Jump 477 Item Bank : Objective Items with Answers 479 Question Bank : Tutorial Problems with Answers 480

12. COMPRESSIBLE FLOW 483 – 509

12.1 Introduction 483 12.2 Sonic Velocity 486 12.3 Mach Number 487 12.4 Isentropic Flow 490 12.5 Stagnation Properties 492 12.6 Normal Shock 493 12.7 Flow through a Converging - Diverging Nozzle 495 12.8 Pitot-Static Probe in a Compressible Flow 498 12.9 Transonic and Supersonic Flows 501 Supplementary Revision Examples 502 Item Bank : Objective Items with Answers 507 Question Bank : Tutorial Problems with Answers 508

13. DIMENSIONAL ANALYSIS AND SIMILITUDE 510 – 539

13.1 Introduction 510 13.2 Dimensions of Physical Quantities 511 13.3 Dimensional Homogeneity 512 13.4 Dimensionless Groups; Buckingham π Theorem 513

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13.5 The Group Method 513 13.6 The Rayleigh’s Method of Indices 515 13.7 Important Force-Ratio Dimensionless Numbers 516 13.8 Applications of the Dimensional Method 519 13.9 Similitude 521 13.10 Modelling Criteria 523 13.11 Distorted Models 530 Item Bank : Objective Items with Answers 534 Question Bank : Tutorial Problems with Answers 536

14. FLUID MACHINES 540 – 588

14.1 Classification on the Basis of General Features 540 14.2 Specific Speed : Type Number in SI Units 542 14.3 Classification on the Basis of Specific Speed 544 14.4 Impulse and Reaction Principles 545 14.5 Energy Transfer: Radial Flow Machines 547 14.6 Centrifugal Machines 549 14.7 Departure from the Ideal Flow 552 14.8 Efficiency of Centrifugal Pumps 553 14.9 Performance of Centrifugal Pumps 556 Experiment: Performance Characteristics of a Centrifugal Pump 560 14.10 Diffusers for Centrifugal Pumps 562 14.11 Operating Point of a Pump 563 14.12 Centrifugal Pumps in Parallels and in Series 564 14.13 Energy Transfer: Axial-Flow Machines 566 14.14 Impulse Turbines : Pelton Wheel 568 14.15 Reaction Turbines : Francis, Deriaz and Kaplan Turbines 574 14.16 Performance of Hydraulic Turbines 575 Experiment: Performance of a Reaction Turbine 578 14.17 Draft Tubes for Reaction Turbines 581 14.18 Cavitation Phenomenon 582 Item Bank : Objective Items with Answers 585 Question Bank : Tutorial Problems with Answers 586

APPENDICES 589 – 604Appendix 1 Review of SI Units 590Appendix 2 Review of Vector Operations 592Appendix 3 Plane Geometrical Figures 594Appendix 4 International Standard Atmosphere 595Appendix 5 Properties of Liquids 596Appendix 6 Properties of Vapours and Gases 598Appendix 7 Basic Properties of Air and Water 600Nomenclature 601Subject Index 605

Learning Objectives inEngineering Fluid Mechanics

On successful completion of all learning activities provided in each chapter, a student will be able to

1 — identify the different states of matter and define a fluid;— differentiate between a system and a control volume in a fluid flow;— define the stress and the rate of strain at a point in a fluid flow;— apply the Newton’s law of viscosity to simple engineering problems;— explain the mechanism of surface tension in liquids and— classify fluids vis-a-vis regimes of flow.

2 — state and prove the Pascal’s law for a static fluid;— derive the hydrostatic law in an incompressible and in a compressible fluid at rest;— determine the hydrostatic force on a given plane or curved surface;— determine the pressure at a desired point in a fluid by employing a single-tube, a U-tube

(upright, inclined or inverted) or a differential manometer;— compute the force of buoyancy on a partially or fully submerged body;— identify the states of equilibrium for a floating body and— determine the surface profile of a liquid in a vessel subjected to a constant acceleration or

a constant rotation,3 — explain the concepts of steady and uniform flow;

— determine the acceleration in a fluid flow;— differentiate between streamlines, pathlines and streaklines;— derive the continuity equation for an incompressible or a compressible flow;— describe a real flow in terms of a stream function;— explain the kinematics of a fluid element and establish the condition for irrotationality and— plot simple flownets in terms of streamlines and velocity potential lines.

4 — establish the Euler’s equation of motion for a two-dimensional steady flow of anincompressible fluid and extend it for three-dimensional viscous flow;

— obtain the Bernoulli equation by integrating the Euler’s equation under appropriateconditions;

— establish the steady flow energy equation and obtain the Bernoulli equation from it;— state the integral momentum equation and the angular momentum equation for simple

engineering flows and— determine the force exerted by a fluid flow on the passage confining it.

5 — determine the velocity at a point in a fluid by employing pitot probes;— estimate the discharge through a pipe by using a venturimeter and— estimate the discharge through an open channel by using a notch.

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6 — describe the flownets and pressure distribution for simple ideal flows, i.e., uniform flow,source, sink, free vortex and their combinations and

— simulate the flow over a long rotating circular cylinder by superimposing a doublet and afree vortex on a uniform flow

7 — describe the conditions under which the flow in a round pipe is laminar or turbulent;— establish the Hagen-Foiseuille equation for laminar flow in a pipe and— determine the viscosity of a liquid by employing viscometers.

8 — explain the development of a boundary layer in an external and in an internal flow;— describe the rationale for the different estimates of boundary layer thickness and— demonstrate the phenomena of turbulence, separation and recirculation of flow and suggest

some means to control the separation of flow.9 — explain the origin of lift and drag forces for flow around an immersed body;

— classify different types of drag;— describe the variation of lift and drag coefficients with .variations in flow;— explain the D’Alembert paradox and the Magnus effect for flow over a cylinder and— estimate the terminal velocity for free fall of a body.

10 — derive an expression for the frictional head loss in pipe flow;— estimate minor losses in pipe transitions; -— draw the energy gradient lines for flow through pipes and— calculate the flow through pipes connected in series and in parallels.

11 — develop an expression for the discharge for uniform flow in an open channel;— draw and interpret the specific energy diagram for a free-surface flow and— describe the formation of a hydraulic jump and estimate the variation of Froude number

and other parameters across a jump.12 — differentiate between various processes of expansion and compression;

— determine the sonic velocity in a fluid;— describe the effect of Mach number in flow;— analyse a normal shock;— describe the flow through a converging-diverging nozzle and— estimate a supersonic velocity by employing a pilot-static probe.

13 — state and apply the Buckingham Pie theorem to arrange a set of given variables intodimensionless groups;

— employ the Rayleigh’s indicial method to determine the functional form of a phenomenonin terms of dimensionless groups;

— state the advantages of the dimensional method, dimensionless groups and dimensionalhomogeneity in engineering and

— describe the principle of similitude and apply it for model testing.14 — classify various types of fluid machines;

— calculate the efficiency of centrifugal pumps, axial flow machines and hydraulic turbines;— describe the characteristic performance of a reaction turbine and centrifugal pump and— calculate the head developed by centrifugal pumps operating in series and in parallels

and finally, apply the principles of fluid mechanics to analyse and to design simplefluid mechanical systems, subsystems and devices!

Engineering Fluid Mechanics

Publisher : SChand Publications ISBN : 9788121901000 Author : K. L. Kumar

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