== FL WORKEDEXAMPLESFOR ENGINEERS Carl Schaschke ~ ~ ~ = ~ MECHANI CS 1 2. WORKED EXAMPLESFOR ENGINEERS Fluid mechanics is an essential component of many engineering degree courses. To the professional engineer, a knowledge of the behaviour of fluids is of crucial ~ I~ importance in cost-effective design and efficient operation of process plant. This 1,1 Carl Schaschke book illustrates the application of theory in fluid mechanics and enables students lIi.~ new to the science to grasp fundamental concepts in the subject.~ ~ ~ II ~ CZJ Written around a series of elementary problems which the author works through n to a solution, the book is intended as a study guide for undergraduates in process ~ ~ II VJ engineering disciplines worldwide.
It will also be of use to practising engineers n with only a rudimentary knowledge of fluid mechanics. ~ I II f @ Concentrating on incompressible, Newtonian fluids and single-phase flow through pipes, chapters include: continuity, energy and momentum; laminar flow and lubrication; tank drainage and variable head flow. A glossary of terms is iU included for reference and all problems use SI units of measurement. } J "' " m II ! I I IChemE Davis Building ISBN 0-85295-405-0 m 165-189 Railway Terrace u Rugby CV21 3HQ, UK 6 J III ill tephone 01788578214 [1ational +441788578214 I I, [icsimile 01788 560833 I JI ilational +44 1788 560833 } I [ ~ u '" .org Fluidmechanics Workedexamples forengineers Carl Schaschke IChemE "".
- -- The information in this book is given in good faith and belief in its accuracy, but does not Preface imply the acceptance of any legal liability or responsibility whatsoever, by the Institution, or by the author, for the consequences of its use 'or misuse in any particular circumstances. All 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, Students commonly find difficulty with problems in fluid mechanics. They recording or otherwise, without the prior may misunderstand what is required or misapply the solutions.
This book is permission of the publisher. intended to help. It is a collection of problems in elementary fluid mechanics with accompanying solutions, and intended principally as a study aid for under- Published by graduatestudentsof chemicalengineering- althoughstudentsof all engineering Institution of Chemical Engineers, disciplines will find it useful. It helps in preparation for examinations, when Davis Building, tackling coursework and assignments, and later in more advanced studies of the 165-189 Railway Terrace, subject.
In preparing this book I have not tried to replace other, fuller texts on Rugby, Warwickshire CV213HQ, UK the subje~t. Instead I have aimed at supporting undergraduate courses and IChemE is a Registered Charity academic tutors involved in the supervision of design projects. In the text, worked examples enable the reader to become familiar with, and @ 1998 Carl Schaschke to grasp firmly, important concepts and principles in fluid mechanics such as Reprinted 2000 with amendments mass, energy and momentum. The mathematical approach is simple for anyone with prior knowledge of basic engineering concepts.
I have limited the prob- ISBN 0 85295 405 0 lems to those involving incompressible, Newtonian fluids and single-phase flow through pipes. There is no attempt to include the effects of compressible and non-Newtc;mian fluids, or of heat and mass transfer. I also held back from more advanced mathematical tools such as vectorial and tensorial mathematics. Many of the problems featured have been provided by university lecturers who are directly involved in teaching t1uid mechanics, and by professional engineers in industry.
I have selected each problem specifically for the light it throws on the fundamentals applied to chemical engineering, and for the confi- dence its solution engenders. The curricula of university chemical engineering degree courses cover the fundamentals of t1uid mechanics with reasonable consistency although, in certain areas, there are some differences in both procedures and nomenclature. Photographs reproduced by courtesy of British Petroleum (page 112), This book adopts a consistent approach throughout which should be recogniz- Conoco (page 98) and Esso UK pic (pages xviii, 60, 140, 192 and 234) able to all students and lecturers. I have tailored the problems kindly contributed by industrialists to safeguard Printed in the United Kingdom by Redwood Books, Trowbridge, Wiltshire commercial secrets and to ensure that the nature of each problem is clear.
There 11 111 is no information or detail which might allow a particular process or company to be recognized. All the problems use SI units. As traditional systems of units are still very much in use in industry, there is a table of useful conversions. Listof symbols Fluid mechanics has ajargon of its own, so I have included a list of definitions.
There are nine chapters. They cover a range from stationary fluids through fluids in motion. Each chapter contains a selected number of problems with solutions that lead the reader step by step. Where appropriate, there are prob- lems with additional points to facilitate a fuller understanding.
Historical refer- ences to prominent pioneers in fluid mechanics are also included. At the end of each chapter a number of additional problems appear; the aim is to extend the reader's experience in problem-solving and to help develop a deeper under- The symbols used in the worked examples are defined below. Where possible, standing of the subject. they conform to consistent usage elsewhere and to international standards.
SI I would like to express my sincere appreciation to Dr Robert Edge (formerly units are used although derived SI units or specialist terms are used where of Strathclyde University), Mr Brendon Harty (Roche Products Limited), Dr appropriate. Specific subscripts are defined separately. Vahid Nassehi (Loughborough University), Professor Christopher Rielly (Loughborough University), Professor Laurence Weatherley (University of Roman Term 51or preferredunit Canterbury), Dr Graeme White (Heriot Watt University), Mr Martin Tims a area of pipe or orifice m2 (Esso UK plc) and Miss Audra Morgan (IChemE) for their assistance in A area of channel or tank m2 preparing this book. I am also grateful for the many discussions with profes- B breadth of rectangular weir m c cQnstant sional engineers from ICI, Esso and Kvaerner Process Technology.
c velocity of sound ms-l The text has been carefully checked. In the event, however, that readers c Ch6zy coefficient m 1I2s-1 uncover any error, misprint or obscurity, I would be grateful to hear about it. c coefficient Suggestions for improvement are also welcome. C concentration gl-1 d diameter m Carl Schaschke D m impeller diameter April 2000 f fraction f friction factor F depth of body below free surface m F force N g gravitational acceleration ms-2 H head m slope of channel k constant L fundamental dimension for length L length m L mass loading kgm-2s-1 m mass kg m mass flowrate kgs-l m mean hydraulic depth m M fundamental dimension for mass n channel roughness m-1/3s IV v .org n number of pipe diameters Ns N rotational speed specific speed rps m3/4s-3/2 Fluidmechanics and P pressure Nm-2 P power W problem-solving P wetted perimeter m Q volumetric flowrate m3s-l r radius m R frictional resistance Nm-2 R radius m S depth m Sn suction specific speed Fluid mechanics forms an integral part of the education of a chemical engineer.
t thickness of oil film mm The science deals with the behaviour of fluids when subjected to changes of t time s pressure, frictional resistance, flow through pipes, ducts, restrictions and T fundamental dimension for time production of power. It also includes the development and testing of theories T torque Nm v devised to explain various phenomena. To the chemical engineer, a knowledge velocity ms-l V volume of the behaviour of fluids is of crucial importance in cost-effective design and m3 W width m efficient operation of process plant. W work w Fluid mechanics is well known for the large number of concepts needed to x principal co-ordinate solve even th~ apparently simplest of problems.
It is important for the engineer x distance m to have a full and lucid grasp of these concepts in order to attempt to solve prob- y principal co-ordinate lems in fluid mechanics. There is, of course, a considerable difference between y distance m studying the principles of the subject for examination purposes, and their appli- z principal co-ordinate cation by the practising chemical engineer. Both the student and the profes- z static head m sional chemical engineer, however, require a sound grounding. It is essential that the basics are thoroughly understood and can be correctly applied.
Greek Many students have difficulty in identifying relevant information and funda- ~ ratio of pipe to throat diameter mentals, particular~y close to examination time. Equally, students may be hesi- 8 film thickness mm tant in applying theories covered in their studies, resulting from either an ~ finite difference incomplete understanding of the principles or a lack of confidence caused by E absolute roughness mm 11 unfamiliarity. For those new to the subject, finding a clear path to solving a pump efficiency 8 angle problem may not always be straightforward. For the unwary and inexperienced, A- friction factor the opportunity to deviate, to apply incorrect or inappropriate formulae or to Il dynamic viscosity Nsm-2 reach a mathematical impasse in the face of complex equations, is all too real.
v kinematic viscosity m2s-1 The danger is that the student will dwell on a mathematical quirk which may be 1t 3.14159 specific purely to the manner in which the problem has been (incorrectly) P density kgm-3 approached. A disproportionate amount of effort will therefore be expended on cr surface tension Nm-l something irrelevant to the subject of fluid mechanics. 't shear stress Nm-2 Students deyelop and use methods for study which are dependent on their <1> friction factor own personal needs, circumstances and available resources. In general, ffi angular velocity radians s-l however, a quicker and deeper understanding of principles is achieved when a VI VB problem is provided with an accompanying solution.
The worked example is a Finally, the application of fluid mechanics in chemical engineering today recognized and widely-used approach to self-study, providing a clear and relies on the fundamental principles largely founded in the seventeenth and logical approach from a distinct starting point through defined steps, together eighteenth centuries by scientists including Bernoulli, Newton and Euler. with the relevant mathematical formulae and manipulation. This method bene- Many of today's engineering problems are complex, non-linear, three- fits the student by appreciation of both the depth and complexity involved in dimensional and transient, requiring interdisciplinary approaches to solution. High-speed and powerful computers are increasingly used to solve complex While some problems in fluid mechanics are straightforward, unexpected problems, particularly in computational fluid dynamics (CFD).
It is worth difficulties can be encountered when seemingly similar or related simple prob- remembering, however, that the solutions are only as valid as the mathematical lems require the evaluation of a different but associated variable. Although the models and experimental data used to describe fluid flow phenomena. There is, solution may require the same starting point, the route through to the final for example, no analytical model that describes precisely the random behaviour answer may be quite different. For example, determining the rate of uniform of fluids in turbulent motion.
There is still no substitute for an all-round under- flow along an inclined channel given the dimensions of the channel is straight- standing and appreciation of the underlying concepts and the ability to solve or forward. But determining the depth of flow along the channel for given parame- check problems from first principles. ters in the flow presents a problem. Whereas the former is readily solved analyti- cally, the latter is complicated by the fact that the fluid velocity, flow area and a flow coefficient all involve the depth of flow.
An analytical solution is no longer possible, thus requiring the use of graphical or trial and error approaches.