Fluid Mechanics Course Research Articles

A Computer-Generated ‘Pseudo-Experiment’ in Fluid Mechanics

The paper presents experience in setting up and running a computer-based alternative to a traditional undergraduate laboratory class as part of an introductory course in fluid mechanics. The ‘pseudo-experiment’ is not a computer simulation but provides each individual student with a realistic set of experimental readings (including likely random errors) for a real set of apparatus on which they have earlier conducted a real ‘hands-on’ experiment, and which was available for them to inspect or operate in their own time. Students were expected to process the results supplied and then write the usual form of full report on the experiment, including of course a full discussion of the results obtained. The results the students obtained were very close to what would have been obtained by real measurement at the flow rate given, and the inclusion of a realistic level of random error ensured that these results varied slightly from student to student, thus inhibiting copying of work. The arrangement eased timetabling problems and provided a significant saving in academic resource while retaining many of the advantages of a real hands-on laboratory class, and enhanced the students' educational experience compared with earlier arrangements. An additional advantage of the system adopted was that each student's correct calculated output was exactly known so that marking could be undertaken by paid postgraduate assistants rather than academic staff.

Philip Gerald Drazin

Philip Gerald Drazin

Physical Hydrodynamics

Physical Hydrodynamics

Review of Environmental fluid mechanics by Hillel Rubin and Joseph Atkinson

Review of <i>Environmental fluid mechanics</i> by Hillel Rubin and Joseph Atkinson

Hydraulic Design Example—Canal and Pipeline Inlet

An example of a hydraulic design project is presented. This design project is intended for a “third year” course in hydraulics, which is the first hydraulics course after the introductory course in fluid mechanics. Students are required to combine canal segments, inlet and outlet structures, gates, and flow measurement structure into a canal system. Students work in groups to complete the design calculations, plans, and oral and written reports.

A First Course in Fluid Mechanics for Civil Engineers

<i>A First Course in Fluid Mechanics for Civil Engineers</i>

Engineering Fluid Mechanics

9R37. Engineering Fluid Mechanics. - WP Graebel (Dept of Mech Eng and Appl Mech, Univ of Michigan, Ann Arbor MI). Taylor &amp; Francis Publ, New York NY. 2001. 676 pp. ISBN 1-560-32711-1. $89.95.Reviewed by AS Paintal (Eng Dept, Metropolitan Water Reclamation District, 100 E Erie St, Chicago IL 60611).This is a text for an introductory course in engineering fluid mechanics. Fluid mechanics is one of the basic courses required for an undergraduate degree in engineering. The purpose of the book is to provide basic theory as well as to develop analytical skills in the engineering students. The book helps the students to get a feel for flow patterns; pressure variations; and continuity, energy, and momentum principles. The book is organized into 12 chapters and seven appendices. The chapters provide orderly development of the subject. Chapter 1 gives a brief introduction of the subject. Fluid properties are defined and procedures for solving engineering problems are suggested. Chapter 2 deals with hydrostatics and pressure variations and distributions in fluids subjected to rigid body accelerations. Chapter 3 is devoted to fluid dynamics. The ideas of control volume and control surface are introduced, and concepts of incompressibility and discharge are defined. The fundamental equations of fluid mechanics in one dimension are formulated using the concepts of conservation of mass, linear momentum, angular momentum, and energy. Application of these equations for problem solving is emphasized. In Chapter 4, the differential equations using the continuity, energy, and momentum concepts are derived in two- and three-dimensions. The concepts of potential flow are also introduced. Chapter 5 deals with the dimensional analysis and model-prototype relationships. Chapters 6 and 7 concern laminar and turbulent flows. The equation for laminar flows between parallel plates and circular tubes are formulated, and the concept of boundary layer is introduced in Chapter 6. The concept is further developed for turbulent boundary layers in Chapter 7. Turbulent flow in pipes is thoroughly analyzed. The chapter also covers drag and lift forces. Chapter 8 considers the hydraulics of open channel, and the effect of gravity on flow is analyzed. Chapter 9 deals with the compressible flow problems and the effect of Mach Number on the flow. In Chapter 10, various flow, pressure, and velocity measurement techniques are evaluated. Chapter 11 is devoted to hydraulic machines. In Chapter 12, suggestions are made for additional study of various engineering disciplines involving the principles of fluid mechanics. There are a number of solved problems included in every chapter to explain the principles involved. At the end of each chapter, a set of unsolved problems is provided for practice. The answers to even-numbered problems are given at the end of the book. There are seven appendices. Appendix A deals with conversion of units and gives useful constants. Appendix B summarizes the fluid properties of water air and other common fluids in British (US) and SI units. Appendix C covers mathematical aids used for solving fluid mechanics problems. Appendix D provides compressible flow tables for air k=1.4. A brief history of fluid mechanics is given in Appendix E. Appendix F’s focus is on the design of a pump system. The purpose is to demonstrate how the design and other broader issues are considered in the design. Engineering Fluid Mechanics provides a balanced treatment of engineering fluid mechanics. The theory as well as problem solving skills are emphasized. The book should be considered for adoption as a text for an introductory undergraduate course in fluid mechanics. It will be useful for engineers working in the area of fluid mechanics or preparing for the examination leading to a professional engineer license.

A first course in fluid mechanics for civil engineers

Book review / Critiques de livres Dr. Gray is presently an Associate Professo in the Department of Civil and Environmental Engineering at West Virginia University at Morgantown in West Virginia. He has considerable experience in teaching fluid mechanics, has published over 100 papers and reports in fluid mechanics, and also has industrial experience. He wrote this text in fluid mechanics for a one-semester course for civil, environmental, and agricultural engineers to provide a narrower focus rather than attempt to cover the whole range of fluid mechanics. Dr. Gray believes that such a narrow focus might motivate the students more readily. This book uses both the US Customary and SI systems of units. This book has 15 chapters and two appendices that deal with Tables of Fluid Properties and Answers to Selected Problems; it also has a Subject Index. The first chapter presents the scope of engineering fluid mechanics — a brief description of many books dealing with fluid mechanics along with a discussion of units. The second chapter treats fluid properties with the discussion of viscosity left to a later chapter. Chapters 3 and 4 present a thorough discussion of the principles of hydrostatics, covering pressure distribution in liquids, manometers, idea of piezometric head, stratified layers, and force exerted on plane surfaces. Discussion of force exerted on curved surfaces and buoyancy is delayed until chapter 14. Chapter 5 presents a discussion of fluid dynamics, starting with the development of the Euler equation along the streamline and its integration to obtain the Bernoulli equation. The author then uses the Bernoulli equation to present and discuss a number of elementary problems like water jets in air, pitot and pitot-static tubes, venturimeter, and sharpcrested weirs. Chapter 5 closes with the development of the Euler equations in the Cartesian system with the Z axis in the vertical direction. Chapter 6 is a rather lengthy presentation of the mass conservation equation. Chapter 7 presents a discussion of viscosity and a detailed derivation of fully developed laminar flor in a circular pipe and ends with a partially complete derivation of the NavierStokes equation in the Cartesian system. Chapter 8 presents a good derivation of the energy equation, which is correctly identified as different from the Bernoulli equation. The idea of the piezometric and total heads is discussed along with some standard problems. Chapter 9 is entitled Pipe Flow 1 and develops the Poiseuille equation using the energy equation and the results derived from chapter 7. It also presents a short discussion of turbulent flow. Chapter 10 presents a brief discussion on dimensional analysis. Pipe Flow 2 constitutes chapter 11, which deals with head loss for turbulent flow in circular pipes, discusses the Moody Diagram, minor losses, and standard pipe flow problems with some comments on turbulent flow in non-circular pipes. The momentum equation is developed in Chapter 12 along with a thorough discussion of a number of problems. Chapter 13 deals with open channel flow. It discusses uniform flow using the Manning equation as well as the friction factor method and nonuniform flow using the idea of the specific head. It also deals with gravity waves including the hydraulic jump. Chapter 15 deals with physical models and similarity. It discusses geometrically similar Reynolds and Froude models as well as some distorted models and ends with brief comments on river models. The treatment of the Euler and Navier-Stokes equations in the Cartesian system could have been made more general by tilting the axes and combining the pressure and body force terms into piezometric gradients. This set of Euler equations could have been integrated to obtain the Bernoulli equation, which would have required the author to present at least a brief treatment of vorticity and potential flow. Further, using the Navier-Stokes equations, the author could have shown how these equations could be simplified to solve a few simple flows, including the Poiseuille equation, in an elegant manner. On the whole, this book is written clearly; it emphasizes engineering relevance, presents numerous worked-out examples, and provides a number of problems for the reader to solve. I think that this book provides a pragmatic introduction to engineering fluid mechanics for students in civil engineering, including environmental and agricultural engineering, and I would recommend this book to them.

A First Course in Fluid Mechanics for Civil Engineers

A First Course in Fluid Mechanics for Civil Engineers

A first course in fluid mechanics for civil engineers

Book review / Critiques de livres Dr. Gray is presently an Associate Professo in the Department of Civil and Environmental Engineering at West Virginia University at Morgantown in West Virginia. He has considerable experience in teaching fluid mechanics, has published over 100 papers and reports in fluid mechanics, and also has industrial experience. He wrote this text in fluid mechanics for a one-semester course for civil, environmental, and agricultural engineers to provide a narrower focus rather than attempt to cover the whole range of fluid mechanics. Dr. Gray believes that such a narrow focus might motivate the students more readily. This book uses both the US Customary and SI systems of units. This book has 15 chapters and two appendices that deal with Tables of Fluid Properties and Answers to Selected Problems; it also has a Subject Index. The first chapter presents the scope of engineering fluid mechanics — a brief description of many books dealing with fluid mechanics along with a discussion of units. The second chapter treats fluid properties with the discussion of viscosity left to a later chapter. Chapters 3 and 4 present a thorough discussion of the principles of hydrostatics, covering pressure distribution in liquids, manometers, idea of piezometric head, stratified layers, and force exerted on plane surfaces. Discussion of force exerted on curved surfaces and buoyancy is delayed until chapter 14. Chapter 5 presents a discussion of fluid dynamics, starting with the development of the Euler equation along the streamline and its integration to obtain the Bernoulli equation. The author then uses the Bernoulli equation to present and discuss a number of elementary problems like water jets in air, pitot and pitot-static tubes, venturimeter, and sharpcrested weirs. Chapter 5 closes with the development of the Euler equations in the Cartesian system with the Z axis in the vertical direction. Chapter 6 is a rather lengthy presentation of the mass conservation equation. Chapter 7 presents a discussion of viscosity and a detailed derivation of fully developed laminar flor in a circular pipe and ends with a partially complete derivation of the NavierStokes equation in the Cartesian system. Chapter 8 presents a good derivation of the energy equation, which is correctly identified as different from the Bernoulli equation. The idea of the piezometric and total heads is discussed along with some standard problems. Chapter 9 is entitled Pipe Flow 1 and develops the Poiseuille equation using the energy equation and the results derived from chapter 7. It also presents a short discussion of turbulent flow. Chapter 10 presents a brief discussion on dimensional analysis. Pipe Flow 2 constitutes chapter 11, which deals with head loss for turbulent flow in circular pipes, discusses the Moody Diagram, minor losses, and standard pipe flow problems with some comments on turbulent flow in non-circular pipes. The momentum equation is developed in Chapter 12 along with a thorough discussion of a number of problems. Chapter 13 deals with open channel flow. It discusses uniform flow using the Manning equation as well as the friction factor method and nonuniform flow using the idea of the specific head. It also deals with gravity waves including the hydraulic jump. Chapter 15 deals with physical models and similarity. It discusses geometrically similar Reynolds and Froude models as well as some distorted models and ends with brief comments on river models. The treatment of the Euler and Navier-Stokes equations in the Cartesian system could have been made more general by tilting the axes and combining the pressure and body force terms into piezometric gradients. This set of Euler equations could have been integrated to obtain the Bernoulli equation, which would have required the author to present at least a brief treatment of vorticity and potential flow. Further, using the Navier-Stokes equations, the author could have shown how these equations could be simplified to solve a few simple flows, including the Poiseuille equation, in an elegant manner. On the whole, this book is written clearly; it emphasizes engineering relevance, presents numerous worked-out examples, and provides a number of problems for the reader to solve. I think that this book provides a pragmatic introduction to engineering fluid mechanics for students in civil engineering, including environmental and agricultural engineering, and I would recommend this book to them.

A ‘Boundary Layer’ Method for Obtaining an Approximate Equation for the Velocity–Time History of an Accelerating Sphere

A sphere starting from rest in a stationary fluid accelerates under the action of gravity and eventually reaches a terminal velocity. The descriptive equation for the acceleration of the sphere is a first order, non-linear, ordinary differential equation, which can be solved using a finite difference scheme. In this study, we present a method (obtained from boundary layer methods) of generating a velocity—time equation to obtain an alternative solution. The method is used to solve a specific example and the results are compared to those obtained with the numerical solution. The comparison yields a small error, and so the polynomial approximation method can be used as an alternative technique to describing the motion of an accelerating sphere. The accelerating sphere problem is usually encountered in a study of flow past immersed objects. Boundary layer methods are usually taught at the graduate level. The advantage of the method presented here is that boundary layer methods can be introduced to undergraduates in a first or second course in fluid mechanics.

Applied dimensional analysis and modeling

This rather large book (of 815 pages) presents a very thorough treatment of dimensional analysis and modeling, covering a broad range of engineering fields. Professor Rozsa has written the first chapter on mathematical preliminaries, which contains a brief discussion of matrices, determinants, and systems of linear equations. Chapters 2–5 discuss the formats for physical relations, dimensional systems, and dimensions. Chapter 6 discusses dimensional homogeneity. The structure of physical relations is discussed at great length in Chap. 7. Chapter 8 shows the development of an efficient method for the construction of dimensionless parameters and introduces a few examples from fluid mechanics. Chapter 9 presents several theorems dealing with the transformations of dimensionless parameters. Chapter 10 discusses the number of dimensionless products of variables with illustrative problems. Chapter 11 presents a discussion on the relevancy of the variables, along with some techniques for identifying physically irrelevant variables. The effectiveness of graphical presentation is discussed in Chap. 12, and forms of the dimensionless relations are discussed in Chap. 13 as to whether the relation between the dimensionless parameters is monomial or non-monomial. If such a monomial relation exists, then some arguments are presented to find the exponents in such a relation. Chapter 14 gives some useful rules and guidelines for sequencing the physical variables in a dimensional set. Chapter 15 discusses problems where dimensions other than mass or force, length, and time occur. One interesting problem is the determination of the optimal location density and location patterns for retail shops. Chapter 16 introduces three ideas to reduce the number of dimensionless groups: (i) reducing the number of physical variables, (ii) increasing the number of dimensions, and (iii) fusing the dimensionless parameters. Chapter 17 looks at dimensional modeling, discussing geometric, kinematic, dynamic, and thermal similarities. This chapter also looks at modeling laws for a whole range of problems, including roasting time for a turkey and comfortable walking speeds for humans and dinosaurs. Chapter 18 presents 43 additional applications, dealing with problems such as axial tensions in a rotating ring, the maximum velocity of an electron in a vacuum tube, the buckling load of a hinged column, existence criteria for black holes, the lateral natural frequency of a cantilever, the diameter of a soap bubble, the velocity of collapse of a row of dominoes, and jamming a circular plug into a non-smooth circular hole. The list of references includes 148 items. There are 8 appendices dealing respectively with (i) recommended names and symbols for some physical quantities, (ii) some more important physical constants, (iii) some more important named dimensionless variables, (iv) notes attached to figures, (v) acronyms, (vi) solutions to problems, (vii) proofs of selected theorems and equations, and (viii) a blank modeling data table. There is also a subject index followed by a surname index. Appendix 3 includes dimensionless numbers such as Beaufort number, Nusselt number, Fourier number, Gratz number, Grashof number, Peclet number, Prandtl number, Rayleigh number, Reynolds number, Schmidt number, Stanton number, Cowling number, Euler number, Froude number, Hartman number, Knudsen number, Strouhal number, Weber number, Snellen number, Mach number, and Cauchy number. This is indeed a rigorous treatment of dimensional analysis, covering vast areas of engineering and physics. Reading the book, one is continuously touched by the contagious enthusiasm and intriguing insight of the author and is entertained by so many interesting anecdotes, quotations, and amusing problems. The treatment of the different topics is very thorough. This reviewer teaches and works in the areas of fluid mechanics and hydraulic engineering and uses dimensional analysis and hydraulic modeling in his work and enjoyed reading this book. Generally, undergraduate students in civil engineering, in their course in fluid mechanics, are introduced to dimensional analysis and then study the principles of hydraulic modeling. Most texts in fluid mechanics have a chapter dealing with these two topics and as such a book like this is perhaps not suitable for them. Even graduate students might find this book far too extensive. But researchers and engineers might find all kinds of interesting problems in this book and as such would benefit from studying this book. This book would be an excellent addition to engineering libraries and consulting offices.

Pipe flow simulation software: A team approach to solve an engineering education problem

THE STUDY OF THE MOTION OF FLUIDS is integral to many engineering disciplines. A first course in fluid mechanics introduces many types of flow, including steady flow through pipe systems. Computer simulations can play a role in the discovery of fluid engineering principles without requiring extensive laboratory facilities or the complicated mathematics associated with the theoretical development. TheFluid Flow Construction Set was developed as an educational tool to introduce engineering students to fluid flow in pipe systems. The software is an interactive tool to explore the fluid flow characteristics of a pipe system by manipulating the physical construction of the system. Both steady (time-independent) and transient (time-dependent) pipe flow can be simulated. The motivation and software design requirements are presented first, followed by specific details on how the objectives of the design tool were met.

Reply [to “Comment on ‘Paradoxes and realities in unsaturated flow theory’ by W. G. Gray and S. M. Hassanizadeh”

The authors are pleased that Miller [this issue] has taken the opportunity to comment on our recent paper [Gray and Hassanizadeh, 1991]. The purpose of that paper was to raise a number of questions concerning the standard interpretation of unsaturated flow phenomena and the mathematical description of those pheiaomena. In particular, the paper raised four issues or paradoxesThe first issue concerns equations of state: May equations of state, typically posed at one scale for a single phase fluid, be applied directly at another scale? In particular, for unsaturated flows, how is saturation incorporated into the equations of state? The second issue addresses the range of values for capillary pressure. The reported range of measured values for capillary pressure in unsaturated flow requires that the pressure in the water phase take on large negative values at low saturations for any soil type. Is this realistic or is this a manifestation of other forces that impact system behavior? How would these other forces be accounted for systemaftcally? The third issue involves equilibrium pressure. Does the equilibrium pressure profile in a fluid phase under unsaturated conditions obey the hydrostatic condition? Does imposition of such a profile neglect bonding effects between the wetting phase and the solid? Finny, the fourth issue raises the question of interfacial effects. The most important physical difference between saturated and unsaturated flow is the presence of interfaces between the fluid phases. Is an unsaturated flow theory that makes use of no governing equations for the distribution of interfacial areas per unit volume complete and capable of describing the system? The comment of Miller [this issue] addresses the second of these issues in isolation from the other paradoxes, an approach that may lead to overlooking the overall problem of obtaining an accurate physical description of unsaturated flow and the mechanisms which drive that flow. Miller has formulated his comments within the framework of physics and physics. The chief difference in these two alternative viewpoints is that in glass bead physics, interfaces between phases are much closer together than in beaker physics. The inteffac!al area per unit volume in glass bead physics is also much greater than for beaker physics. The approach of the authors, on the other hand, examines phenomena from two different scales. At the microscale, the fluid phases are governed by the conservation. equations generally encountered in a standard fluid mechanics course. However, solution of these equations at

The Fluid Jetster: A Water‐Powered Wheeled Vehicle

AbstractThe fluid jetster is a water‐powered, wheeled vehicle designed, constructed, and tested by students in a fluid mechanics course in the Civil Engineering (CE) curriculum at Oregon State University during the junior year. Students design and build a fluid jetster powered solely by water from a reservoir connected to a nozzle and mounted on a wheeled platform. The project includes both theoretical and experimental design requirements. This project provides a significant learning opportunity for students to apply the fundamental principles of fluid mechanics, to compare both Lagrangian and Eulerian dynamics, to work with peers, and to experience the connections between theory and design applications.

Formation d'ingénieur en Hydraulique et Mécanique des fluides : exemple de l'enseignement à l'Ecole Nationale des Ponts et Chaussées

The present paper deals with the complement aspects of , which results from the increasing use of the general Fluid Mechanics methods white solving Hydraulics problems. The paper emphasizes how these complementary aspects are used in the various subtopics of the Applied Fluid Mechanics course at Ecole Nationale des Ponts et Chaussees .

Computer modeling of superimposed inviscid flows on a microcomputer

Complex flow patterns can be simulated in inviscid flow theory through the superposition of simple flows such as sinks, sources, and uniform flow. The resulting flows are valuable in modeling the flow of fluids at high Reynolds numbers and may be used to simulate the flow over airfoils, aircraft fuselages, ship hulls, and circular pipes in heat exchangers. A computer simulation program has been developed that models inviscid flow patterns and plots the resulting streamlines and equipotential lines on a microcomputer monitor. The program allows the user to superimpose doublets, sinks, sources, uniform flow, and vortices in any desired pattern. The code can also calculate and plot the inviscid velocity and pressure distribution at any point in the flow. A wide choice of singular 2-D flows can be superimposed with user-specified strengths, positions, and orientation angles. The program has been successfully used in undergraduate and graduate fluid mechanics courses and has been used to develop the pressure distributions around submerged structures.

Basic Elements in a Fluid Mechanics Laboratory Experience: An Engineering Science Approach

Experiments for a first fluid mechanics course are described. The basic concepts of pressure and velocity as the primitive variables, the control volume equations and the field equations with Reynolds number dependent properties are reinforced in these experiments. The use of such experiments, as the experimental background for future lecture instruction, is emphasized.

A Survey of Fluid Mechanics Education of Mechanical Engineers

Results are presented from a national survey of fluid mechanics courses taught in Mechanical Engineering Departments of U. S. institutions for the academic year 1975–1976. The respondent sample included 91 institutions of widely varying character. Data from five groups of fluids courses are discussed: required undergraduate courses including basic and advanced level; advanced level undergraduate elective courses; graduate level courses; and continuing education courses. Primary educational features reviewed include subject area, textbook used, relative emphasis between theory and applications, credit hours, relative use of multiple course sequence, and amount of laboratory instruction. Guidelines for future surveys are also included.

A C.A.L. course in fluid mechanics and heat transfer†

Under the auspices of the National Development Programme in Computer‐Assisted Learning, a C.A.L. course entitled ‘ Fundamentals of Fluid Mechanics and Heat Transfer ‘ has been given at Imperial College London to final‐year B.Sc. students in Mechanical Engineering in the session 1974/75 and 1975/76. The course consisted of 20 lectures and an equal number of periods devoted to the solution and discussion of a carefully‐selected set of illustrative problems which the students tackled with the aid of computer programmes specially developed for the purpose. In this paper, the authors present (a) a brief description of the course, with special emphasis on the role played by the computational component, (b) an outline of the methods used to assess the students’ understanding of the material taught and (c) a description of the methods, both subjective and objective, used to evaluate the success of the course. † Paper presented at the conference on ‘ Computers in Higher Education’ held at Loughborough University o...