Fluid Mechanics for
Chemical Engineering
Mathieu Mory
,First published 2011 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as
permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced,
stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers,
or in the case of reprographic reproduction in accordance with the terms and licenses issued by the
CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the
undermentioned address:
ISTE Ltd John Wiley & Sons, Inc.
27-37 St George’s Road 111 River Street
London SW19 4EU Hoboken, NJ 07030
UK USA
www.iste.co.uk www.wiley.com
© ISTE Ltd 2011
The rights of Mathieu Mory to be identified as the author of this work have been asserted by him in
accordance with the Copyright, Designs and Patents Act 1988.
____________________________________________________________________________________
Library of Congress Cataloging-in-Publication Data
Mory, Mathieu.
Fluid mechanics for chemical engineering / Mathieu Mory.
p. cm.
Includes bibliographical references and index.
ISBN 978-1-84821-281-7 (hardback)
1. Chemical processes. 2. Fluid dynamics. I. Title.
TP155.7.M673 2011
660'.29--dc22
2010048940
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-84821-281-7
Printed and bound in Great Britain by CPI Antony Rowe, Chippenham and Eastbourne.
, Table of Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
PART I. ELEMENTS IN FLUID MECHANICS . . . . . . . . . . . . . . . . . . . . . . 1
Chapter 1. Local Equations of Fluid Mechanics . . . . . . . . . . . . . . . . . 3
1.1. Forces, stress tensor, and pressure . . . . . . . . . . . . . . . . . . . . . . 4
1.2. Navier–Stokes equations in Cartesian coordinates . . . . . . . . . . . . . 6
1.3. The plane Poiseuille flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4. Navier–Stokes equations in cylindrical coordinates: Poiseuille flow
in a circular cylindrical pipe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5. Plane Couette flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.6. The boundary layer concept . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.7. Solutions of Navier–Stokes equations where a gravity field is present,
hydrostatic pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.8. Buoyancy force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.9. Some conclusions on the solutions of Navier–Stokes equations . . . . . 26
Chapter 2. Global Theorems of Fluid Mechanics . . . . . . . . . . . . . . . . 29
2.1. Euler equations in an intrinsic coordinate system . . . . . . . . . . . . . 30
2.2. Bernoulli’s theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3. Pressure variation in a direction normal to a streamline. . . . . . . . . . 33
2.4. Momentum theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5. Evaluating friction for a steady-state flow in a straight pipe . . . . . . . 38
2.6. Pressure drop in a sudden expansion (Borda calculation) . . . . . . . . 40
2.7. Using the momentum theorem in the presence of gravity. . . . . . . . . 43
2.8. Kinetic energy balance and dissipation . . . . . . . . . . . . . . . . . . . 43
2.9. Application exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Exercise 2.I: Force exerted on a bend . . . . . . . . . . . . . . . . . . . . . . 47
, vi Fluid Mechanics for Chemical Engineering
Exercise 2.II: Emptying a tank . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Exercise 2.III: Pressure drop in a sudden expansion and heating. . . . . . 48
Exercise 2.IV: Streaming flow on an inclined plane . . . . . . . . . . . . . 49
Exercise 2.V: Impact of a jet on a sloping plate . . . . . . . . . . . . . . . . 50
Exercise 2.VI: Operation of a hydro-ejector . . . . . . . . . . . . . . . . . . 51
Exercise 2.VII: Bypass flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Chapter 3. Dimensional Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.1. Principle of dimensional analysis, Vaschy–Buckingham theorem . . . 56
3.1.1. Example – the oscillating pendulum. . . . . . . . . . . . . . . . . . . 60
3.2. Dimensional study of Navier–Stokes equations . . . . . . . . . . . . . . 61
3.3. Similarity theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.4. An application example: fall velocity of a spherical particle in a
viscous fluid at rest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.4.1. Application of the Vaschy–Buckingham theorem. . . . . . . . . . . 65
3.4.2. Forces exerted on the ball . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.4.3. The hydrodynamic force opposing the particle’s movement
relative to the fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.4.4. Fall velocity for a small Reynolds number . . . . . . . . . . . . . . . 67
3.4.5. Fall velocity for a large Reynolds number . . . . . . . . . . . . . . . 68
3.5. Application exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Exercise 3.I: Time of residence and chemical reaction in a stirred
reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Exercise 3.II: Boundary layer on an oscillating plate. . . . . . . . . . . . . 69
Exercise 3.III: Head capacity curve of a centrifugal pump . . . . . . . . . 70
Chapter 4. Steady-State Hydraulic Circuits . . . . . . . . . . . . . . . . . . . . 73
4.1. Operating point of a hydraulic circuit . . . . . . . . . . . . . . . . . . . . 73
4.2. Steady-state flows in straight pipes: regular head loss. . . . . . . . . . . 78
4.3. Turbulence in a pipe and velocity profile of the flow . . . . . . . . . . . 81
4.4. Singular head losses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.5. Notions on cavitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.6. Application exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Exercise 4.I: Regular head loss measurement and flow rate in a pipe . . . 88
Exercise 4.II: Head loss and cavitation in a hydraulic circuit . . . . . . . . 89
Exercise 4.III: Ventilation of a road tunnel . . . . . . . . . . . . . . . . . . 91
Exercise 4.IV: Sizing a network of heating pipes . . . . . . . . . . . . . . . 92
Exercise 4.V: Head, flow rate, and output of a hydroelectric
power plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Chemical Engineering
Mathieu Mory
,First published 2011 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as
permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced,
stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers,
or in the case of reprographic reproduction in accordance with the terms and licenses issued by the
CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the
undermentioned address:
ISTE Ltd John Wiley & Sons, Inc.
27-37 St George’s Road 111 River Street
London SW19 4EU Hoboken, NJ 07030
UK USA
www.iste.co.uk www.wiley.com
© ISTE Ltd 2011
The rights of Mathieu Mory to be identified as the author of this work have been asserted by him in
accordance with the Copyright, Designs and Patents Act 1988.
____________________________________________________________________________________
Library of Congress Cataloging-in-Publication Data
Mory, Mathieu.
Fluid mechanics for chemical engineering / Mathieu Mory.
p. cm.
Includes bibliographical references and index.
ISBN 978-1-84821-281-7 (hardback)
1. Chemical processes. 2. Fluid dynamics. I. Title.
TP155.7.M673 2011
660'.29--dc22
2010048940
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-84821-281-7
Printed and bound in Great Britain by CPI Antony Rowe, Chippenham and Eastbourne.
, Table of Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
PART I. ELEMENTS IN FLUID MECHANICS . . . . . . . . . . . . . . . . . . . . . . 1
Chapter 1. Local Equations of Fluid Mechanics . . . . . . . . . . . . . . . . . 3
1.1. Forces, stress tensor, and pressure . . . . . . . . . . . . . . . . . . . . . . 4
1.2. Navier–Stokes equations in Cartesian coordinates . . . . . . . . . . . . . 6
1.3. The plane Poiseuille flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4. Navier–Stokes equations in cylindrical coordinates: Poiseuille flow
in a circular cylindrical pipe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5. Plane Couette flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.6. The boundary layer concept . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.7. Solutions of Navier–Stokes equations where a gravity field is present,
hydrostatic pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.8. Buoyancy force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.9. Some conclusions on the solutions of Navier–Stokes equations . . . . . 26
Chapter 2. Global Theorems of Fluid Mechanics . . . . . . . . . . . . . . . . 29
2.1. Euler equations in an intrinsic coordinate system . . . . . . . . . . . . . 30
2.2. Bernoulli’s theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3. Pressure variation in a direction normal to a streamline. . . . . . . . . . 33
2.4. Momentum theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5. Evaluating friction for a steady-state flow in a straight pipe . . . . . . . 38
2.6. Pressure drop in a sudden expansion (Borda calculation) . . . . . . . . 40
2.7. Using the momentum theorem in the presence of gravity. . . . . . . . . 43
2.8. Kinetic energy balance and dissipation . . . . . . . . . . . . . . . . . . . 43
2.9. Application exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Exercise 2.I: Force exerted on a bend . . . . . . . . . . . . . . . . . . . . . . 47
, vi Fluid Mechanics for Chemical Engineering
Exercise 2.II: Emptying a tank . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Exercise 2.III: Pressure drop in a sudden expansion and heating. . . . . . 48
Exercise 2.IV: Streaming flow on an inclined plane . . . . . . . . . . . . . 49
Exercise 2.V: Impact of a jet on a sloping plate . . . . . . . . . . . . . . . . 50
Exercise 2.VI: Operation of a hydro-ejector . . . . . . . . . . . . . . . . . . 51
Exercise 2.VII: Bypass flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Chapter 3. Dimensional Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.1. Principle of dimensional analysis, Vaschy–Buckingham theorem . . . 56
3.1.1. Example – the oscillating pendulum. . . . . . . . . . . . . . . . . . . 60
3.2. Dimensional study of Navier–Stokes equations . . . . . . . . . . . . . . 61
3.3. Similarity theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.4. An application example: fall velocity of a spherical particle in a
viscous fluid at rest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.4.1. Application of the Vaschy–Buckingham theorem. . . . . . . . . . . 65
3.4.2. Forces exerted on the ball . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.4.3. The hydrodynamic force opposing the particle’s movement
relative to the fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.4.4. Fall velocity for a small Reynolds number . . . . . . . . . . . . . . . 67
3.4.5. Fall velocity for a large Reynolds number . . . . . . . . . . . . . . . 68
3.5. Application exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Exercise 3.I: Time of residence and chemical reaction in a stirred
reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Exercise 3.II: Boundary layer on an oscillating plate. . . . . . . . . . . . . 69
Exercise 3.III: Head capacity curve of a centrifugal pump . . . . . . . . . 70
Chapter 4. Steady-State Hydraulic Circuits . . . . . . . . . . . . . . . . . . . . 73
4.1. Operating point of a hydraulic circuit . . . . . . . . . . . . . . . . . . . . 73
4.2. Steady-state flows in straight pipes: regular head loss. . . . . . . . . . . 78
4.3. Turbulence in a pipe and velocity profile of the flow . . . . . . . . . . . 81
4.4. Singular head losses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.5. Notions on cavitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.6. Application exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Exercise 4.I: Regular head loss measurement and flow rate in a pipe . . . 88
Exercise 4.II: Head loss and cavitation in a hydraulic circuit . . . . . . . . 89
Exercise 4.III: Ventilation of a road tunnel . . . . . . . . . . . . . . . . . . 91
Exercise 4.IV: Sizing a network of heating pipes . . . . . . . . . . . . . . . 92
Exercise 4.V: Head, flow rate, and output of a hydroelectric
power plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
