Engineering fluid mechanics

p A Aswatha Narayana

K N Seetharamu

E ngineering Fluid M echanics

Engineering Fluid Mechanic

PA Aswatha Narayana

K N Seetharamu

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Alpha Science International Ltd.

O xford, U.K.

p A Aswatha Narayana

K N Seetharamu

Professors (Retd)

Indian Institute of Technology. M adras

Chennai, India

P resently ai

S ch o o l o f M e c h a n i c a l E n g i n e e r in g

University of Science M alaysia

Copyright © 2004

First Reprint 2007

Alpha Science International Ltd.

7200 The Quorum, Oxford Business Park North

Garsinaton Road, Oxford 0 X 4 2JZ. U.K.

www.alphasci.com

All rights reserved. N o part o f this publication may be reproduced, stored in a retrieval

s>'stem. or transm itted in any form or bv any means, electronic, mechanical, photocopv ine.

recording or otherwise, without prior written permission of the publisher.

Printer from the camera-ready copy provided by the Authors.

ISBN 978-1-84265-101-8

Printed in India

Dedicated to our families

Siiantha .4. Sarayana, R aghu, Shoba and B adrinath

and

Uma Seetharam u, A n il and \ ’ani

Foreword

I am very happy to provide this Foreword to the Book on “Engineering

Fluid Mechanics”, by Professor p.A. Aswatha Narayana and Professor

K.N. Seetharamu. Both o f them have worked at the Indian Institute of

Technology, Chennai for about three decades. Even though they belonged

to different Department, still they were able to collaborate on a large

number o f projects and academic activities. This Book is a result o f one

such collaboration.

This Book is bom e out o f the notes and video lecture material prepared by

the authors for teaching Under-Graduate and Post-Graduate courses on

Fluid M echanics at IIT, Madras. They have revised it taking into

consideration their expertise in Teaching and Research, as well as on the

basis o f the feedback received on these courses.

The Book contains twenty chapters, distributed over topics on

Fundamentals and Applications. The authors have also given a large

number o f worked problems as well as problems to be solved. It is

believed that the Text Book would be useful for students in Mechanical,

Aerospace, Civil and Chemical Engineering.

I have no doubt that considering the Knowledge, Experience and Expertise

of the authors, their Text Book would serve a useful purpose for the benefit

of Engineering Students.

R. NATARAJAN

Chairman

All India Council for Technical Education

New Delhi

Preface

This book IS an outcome o f collection of notes and video lecture material

prepared bv the authors for teaching first and second levels of

undersraduate and first level post graduate courses on Fluid M echanics at

Indian Institute o f Technology Madras (IITM). The notes have been

upei'aded at least three times o \e r the past few years based upon

experience in teaching and research.

Durins the course o f preparing the lecture notes, the authors observed

that there is paucifs' o f undersraduate fluid mechanics textbooks suitable

for the IIT curriculum. W ith all round restructurina o f the courses to cater

to the rapid advances made in defence, aerospace, environmental and

related energy sectors, the syllabus therein on fluid mechanics in all

enameermg institutions is also beine uperaded. Authors also feel that the

undersraduate textbook should also contain some advanced material. In the

preparation o f this elem entaụ' book, we do not claim any orisinaliụ’ but

for the experience in research and teaching which enabled us to explain a

few things better. During the preparation of the lecture material, the books

authored by Vijay Gupta and Santosh K.Gupta and also by K.M uraldhar

and G.Biswas h a \e been extensively used among others. Hence in some

chapters o f the present book, at certain places their line of presentation

\\ ould have appeared. We are ver\’ much thankful to the authors of the

above books.

The contents o f the book are presented in 21 chapters. Basic materials

are lucidly presented with assumptions made and the method o f solution

si\en. Application of Bernoulli's equation, momentum theorem,

turbomachmes and dimensional analysis are dealt in greater detail.

Mechanics o f laminar and turbulent flows, boundan- layer theon’.

incompressible inviscid flows, compressible flows are presented in greater

depth not commonly found in many aeneral textbooks. Inưoduction to

w ave hydrod\Tiam ics, experimental techniques, com putational fluid

d)Tiamics and anah'sis of experimental uncertaint>- are also covered. Since

one o f the prim an- goals in fluid m echanics IS the capabilin- to desiCT

encineerine systems and processes, this aspect has also been treated. A

tairl>- laree set of worked problems tblloued by unsolved problems are

included to help the student to de\elop his understanding and also intended

to train an engineer to take up quickly the analysis o f many difficult fluid

mechanics problems.

The preparation of this textbook has been possible with support from

various quarters. Authors thank the Centre for Continuing Education of

Indian Institute of Technology Madras for providing the necessar>’ support

and encouragement and also the Educational Technology Cell to have the

initial material in the form of video lectures. Dr.B.S.V.Patnaik our former

research scholar and presently at NUS, Singapore attended all the video

lectures and encouraged us to bring the material in the form of a textbook.

We are thankful to him. We thank Prof.R.Natarajan, Chaiưnan, All India

Council for Technical Education and formerly Director of Indian ửistitute

of Technology, Madras for providing the Foreword and also the

encouragement rendered at IIT Madras .The authors would like to express

their gratitude to Mr.N.K.Mehra and Mrs. Anupama Jauhry for their

interest in publishing this book. Five chapters have been added to the

original draft after the first author joined the School of Mechanical

Engineering, University of Science Malaysia (USM). The authors thank

Dr. Zainal Alimuddm, the previous Dean and Dr.Zaidi Mohd. Ripin. the

Dean of the School of Mechanical Engineering for their encouragement.

Authors are thankful to Mr.Vidya Acharyulu who was working with the

first author as a Project Assistant at IIT Madras for coordinating the whole

work from IIT Madras and USM Engineering Campus. Authors would like

to place on record the sendees of Mrs. Lalitha and Mrs. Godhamani for

their help m typing the material, Mr.Jeevanandham of IIT Madras in

making the necessary drawings, and Mr. Ooi Chun Keang of USM for his

help. Authors are indebted to Mr. Tan Chun Wai and Miss Norasmah

Wahab for their enthusiastic help in tying the lose ends in the final stages

and also for making the final print out possible at USM.

Suggestions and critical comments are welcome from the readers.

USM Engineering Campus

Nibong Tebal. Penang

Malaysia

P. A. Aswatha N'arayana

(paa_iitm(0:hotmail.com)

K. N. Seetharamu

(knseetharamu^'hotmail.com)

Contents

Foreword 'ii

Preface iv

1. Introduction 1

1.1 General Introduction 1

1.2 Trends in Fluid Mechanics 2

1.3 Definition of a Fluid ?

1.4 Concept of Continuum 4

1.5 Dimensions and I'nus 6

1.5.1 SI Units (S>siems International d’Unites) 6

1.5.2 Basic L'nits 6

1.5.3 Den%edL'nits 6

1.6 Basic Equations

1." Basic Definiiions

1 . 1 Mass ■

1.“.2 Density

1 .".3 Specific Weieht s

1. " 4 Specific N'olume s

1.~.5 Specific G ra\m ' s

s Conưol S\‘Stem Analvsis s

Control \ olume Approach 9

10 Co-ordinate System 9

11 Laeraneian and Eulenan Descnption 10

12 One-Dimensional. T\\o-Dimensional and Tlirie￾Dimensional Flo\^ s 11

13 L'nifomi Flou 11

14 Stead\ and Unstead\ Flow 11

15 Flow Pattern - Sưeamlines. Sữeaklines and Padi'inei ’i -

16 N'elocin and Acceleration 13

1" Bod\ and Surface Forces 15

IS Laminar and Turbulent Flows 15

niuỉinìĩh c Problems 16

Problems lo hi solvCii 21