Hydraulics R. S. Khurmi

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A TEXTBOOK OF

Hydraulics, Fluid Mechanics and Hydraulic Machines

For the Students oJ“De free iinJ Diploma Courses

(SI UNITS)

R.S. KIIURMI

Preface to the

Nineteenth Edition

I feel very much elevated in prese'iting the new edition of this standard treatise .

The favourable and warm reception, which the previous editions and reprints of this popular book

has enjoyed all over India and abroad has been a matter of great satisfaction for me.

The present edition of this treatise has been rewritten in S.I. units and brought up-to-date. Lot

of useful changes have been incorporated in this volume to widen its scope and utility. About lIXl

examples. which have been carefully selected from the recent examination papers of

various universities and examining bodies, have been solved and systematically graded in this

volume.

1 wish to express my sincere thanks to numerous professors and students for their valuable

suggestions and recommending the book to their students and friends. I hope, that they will conunue

to patronise this standard treatise in the future also.

Any errors, omissions and suggestions for the improvement of this volume, brought to my notice,

will be thankfully acknowledged and incorporated in the next edition.

R. S. Khurmi

Preface to the Eleventh Edition

1 feel very much satisfied in presenting the eleventh edition of this standard treatise. The

favourable and warm reception, which the previous editions and reprints of this popular book has

enjoyed all over India and abroad has been a matter of great satisfaction for me. The revised

edition of this treatise has been rewritten in S.I. units and M.K.S. units.

The mistakes, which had crept in, have been eliminated. It is earnestly hoped that the book will

continue to cater the loi.g-fell need of the teachers and students of all the Indian and

Foreign Universities.

Any errors, omissions and suggestions for the improvement of this volume, brought to my notice,

will be thankfully acknowledged and incorporated in the next edition.

R. S. Khurmi

Preface to the First Edition

I take an opportunity to present this standard treatise entitled as ‘A Text Book of Hydraulics,

Fiuid Mechanics and Hydraulic Machines’ to the students of Degree and Diploma classes in M.K.S.

units. The object of this book is to present the subject matter in a most concise, compact,

to-the-point and lucid manner.

While writing the book. I have always kept in mind the examination requirements of the students

of Civil Engineering as well as Mechanical Engineering. 1 have also constantly kept in mind the

requirements of other engincering siudents, who are always interested to have an up-to-date and

latestinformation, by incorporating the research work conducted in various countries on allied

topics; available from numerous specialised technical books, papers and periodicals. Thus the book

will provide the students a necessary insight into the subject, and will prepare theñi adequately

for their examinations.

To make the book more useful at all levels, it has been written in an easy stylc and such a simple

manner, lhat even an average student can grasp the subject independently. Every carc has heen

taken to make the book as self-explanatory as possible throughout. The rigorous mathematical steps

have been replaced by simple treatments. The subject matter has been amply illustrated hy

Incorporating

a good number of solved and well graded examples or almosl every s'arietj’. Most of these c xamples

are taken from the recent examlFl2tionpapers of Indian as well as foreign univer.sitiCS and

professional examining bodies. .o make lhe s:udents familiar with the types of questions, usually.

set in their examinationsA. t the end of each topic, a few exercises have been added, for the

sludenls to solve ih•m independently.Answer, along with hints wherever necessary, have been

provided. But it is too much to hope that these are entirely free from errors.

Although every care has been taken to check mistakes and misprints. yet it is di fficult to claim

perfection. Any errors omissions and suggestions. for lhe improvement of this volume brought to my

notice, wf1! be thankfully acknowledged and incorporated in the next edition.

To make the book more useful at all levels, it has been written in an easy stylc and such a simple

manner, lhat even an average student can grasp the subject independently. Every carc has heen

taken to make the book as self-explanatory as possible throughout. The rigorous mathematical steps

have been replaced by simple treatments. The subject matter has been amply illustrated hy

Incorporating

a good number of solved and well graded examples or almosl every s'arietj’. Most of these c

xamples

are taken from the recent examlFl2tion papers of Indian as well as foreign univer.sitiCS and

professional examining bodies. .o make lhe s:udents familiar with the types of questions,

usually. set in their examinations. At the end of each topic, a few exercises have been

added, for the sludenls to solve ih•m independently. Answer, along with hints wherever necessary,

have been provided. But it is too much to hope that these are entirely free from errors.

Although every care has been taken to check mistakes and misprints. yet it is di fficult to

claim perfection. Any errors omissions and suggestions. for lhe improvement of this

volume brought to my notice, wf1! be thankfully acknowledged and incorporated in the next

edition.

K. S. Kliurriii

Contents

S.Nu.

Introduction

2. Fluid Pressure and its Measurement

3. Hydrostatics

4. Applications nf Hydrostatics

10.

- 11.

12.

13.

14.

13.

16.

17,

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

Equilibrium of nearing Bodies

Hydrokinematics

Bemoulli’s Equaiion and its Applications

Flow Through Orifices (Measurement of Discharged Flow; Through Orifices (Measurement of Time)

Flow' Through Mouthpieces

Flow Over Notches Flow Over Weirs

Flow' Through Simple Pipcs Flow Through Compound Pipcs Flow Through Nozzles

Uniform Flow Through Open Channels

hon-Uniform Flow Through Open ChanncTs Viscous Flow

Viscous Resistance

Fluid Masses Subjected to Acceleration Voncx Flow

Mechanics of Compressible Flow Compressiblc Flow of Fluids Floy' Around Immersed Bodies

Dimensional Analysis

Model Analysis (Undistorted Models) Model Analysis (Distorted Models)

107

116

138

153

172

194

210

. 231

253

270

284

310

. 333

. 350

363

373

385

394

. 454

28. Non-DimcnsionaI Constants

29. Impacl of Jets

30. Jet Propulsion

31. Water Wheels

32. Impulse Turbines

33. Reaction Turbines

34.- Performance of Turbi.oes

35. Centrifugal Pumps

36. Reciprocating Pumps

37. Performance of Pumps Pumping Devices

39. Hydraulic Systems

Index

463

. 471

. 489

. 499

. . . .808

. 528

. 561

. 582

. 602

- .h32

. 645

651

. 661

Introduction

1. lniraduc-iiun. 2. Brjtinnifl,9 mid Devvliiyment ufihe Subject. 3. Fundamental Units.

4. Derirrd Units. 5. 5./. (inferr1nfLPttTf S)'ffem r/ Units}. b. Petre. 7.

Kilriyram. R. SeCund. 9. Prrsenta*oy of Unitx and their Values. 10. Rules fur

S.1. Units. 1.1. Liquids and iheir Properties. 12. Density of l¥aier.

13. Syed:ifi Weight o1 Water. IN. Sfiec r C rarity iif l¥aier. IS.

Coinpressibility of I,Yaler. J6. SuJnce Ten.sion of Writer. 7.7. Capillurii y of

Wmer. I R. Viscosity of Waier. 19. 1-useful Data. 20. Force. 2J. Resultant

Fnrc'e. 22 Cvmyosiliuu ‹!f Furce i. 23. Parallelogram Law oJ Forces. 24. Triangle

Law oJ F‹›ri es. 2S. PulyXon Aux' ‹›f Fun es. 25. L‹»vs nf AY‹›iian. 2.7.

Newton ’s dir‹r Loss' nf Malion. 2d. /\/rn'/r›n‘8 Secund £ow c/ 4fcriozt. “22. NeWon 's

Third Law'of Mption. 30. hark. 3I. 7'owrr.

32. Energy. 33. Law of' Consewaiion o/ £nergy. 34. Scalars and VecforS.

1.1 Introduction

The word ‘Hydraulics’ has heen derived front a Greek word ‘Hudour’, which means water.

Thus the subject uf Hydraulics may be dc•tined as that branch of Engineering-science, which

deals with water (at rest or in motion). The .subject of’ Fluid Mechanics may be defined as the

mechanics o1’ fluids (including waier). The suhject Hydraulic Machines may be defined

as that branch of Engineering-science, which deals wiih thc• machines run by water under

some head, or raising the water to higher levels.

In the text of this book some olher liquids, in addition to water, will also be dealt with,

But, in

general, the given liquid will be assumed to be water, unless specified otherwise.

1-2 Beginning and Development of the Subject

It will be interesting to know as to how early lhe man had been curious to know about the earth

and lho varit›us prt›ccsses going ‹in it. As a inatief of‘ fact, sincc the dim ages of

pre-historic times, the iiiaii h.is l›ccii pr:ictisiiip the :irt t›l’ciibinecring. Ant1 he

snarled erecting very simple and ordinary lypcx t›l’ .strol litre.s (r.,p.. tligp•in;i wells

and making water courses for water supply and irrigation purpti.ses) li›r hix

live1ihot›d. W itli the passage of lime the man, entirely on the basis pf his practical

experience and ctiinnion-sense, created a l'ew thumb rules to serve as a guide for erecting very

ordinary types of structures.

It is only since the human progress had reached its e›’olutionary hei*hi. we call the

dawn of civ'il ization, the man actually started to desi gn and build the structurcs accordi np

to his r••quirements. Since then, the man had been very eager to know more and more

about the various aspKts of his structures, especially regarding their uses and smooth

work ability'. Experience taught him, and he continued to make progress in the art of

engineering bit by bit.