Eou Vectors Tensors And The Basic Equations Of Fluid Mechanics
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Eou Vectors Tensors And The Basic Equations Of Fluid Mechanics
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Author : Rutherford Aris
language : en
Publisher:
Release Date : 1990
Eou Vectors Tensors And The Basic Equations Of Fluid Mechanics written by Rutherford Aris and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.
Vectors Tensors And The Basic Equations Of Fluid Mechanics
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Author : Rutherford Aris
language : en
Publisher: Courier Corporation
Release Date : 2012-08-28
Vectors Tensors And The Basic Equations Of Fluid Mechanics written by Rutherford Aris and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-28 with Mathematics categories.
Introductory text, geared toward advanced undergraduate and graduate students, applies mathematics of Cartesian and general tensors to physical field theories and demonstrates them in terms of the theory of fluid mechanics. 1962 edition.
Vectors Tensors And The Basic Aquations Of Fluid Mechanics
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Author :
language : en
Publisher:
Release Date : 1962*
Vectors Tensors And The Basic Aquations Of Fluid Mechanics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962* with categories.
Tensor Analysis And Continuum Mechanics
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Author : Wilhelm Flügge
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Tensor Analysis And Continuum Mechanics written by Wilhelm Flügge and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
Through several centuries there has been a lively interaction between mathematics and mechanics. On the one side, mechanics has used mathemat ics to formulate the basic laws and to apply them to a host of problems that call for the quantitative prediction of the consequences of some action. On the other side, the needs of mechanics have stimulated the development of mathematical concepts. Differential calculus grew out of the needs of Newtonian dynamics; vector algebra was developed as a means . to describe force systems; vector analysis, to study velocity fields and force fields; and the calcul~s of variations has evolved from the energy principles of mechan ics. In recent times the theory of tensors has attracted the attention of the mechanics people. Its very name indicates its origin in the theory of elasticity. For a long time little use has been made of it in this area, but in the last decade its usefulness in the mechanics of continuous media has been widely recognized. While the undergraduate textbook literature in this country was becoming "vectorized" (lagging almost half a century behind the development in Europe), books dealing with various aspects of continuum mechanics took to tensors like fish to water. Since many authors were not sure whether their readers were sufficiently familiar with tensors~ they either added' a chapter on tensors or wrote a separate book on the subject.
Applications Of Vector Analysis And Complex Variables In Engineering
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Author : Otto D. L. Strack
language : en
Publisher: Springer Nature
Release Date : 2020-04-18
Applications Of Vector Analysis And Complex Variables In Engineering written by Otto D. L. Strack and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-18 with Technology & Engineering categories.
This textbook presents the application of mathematical methods and theorems tosolve engineering problems, rather than focusing on mathematical proofs. Applications of Vector Analysis and Complex Variables in Engineering explains the mathematical principles in a manner suitable for engineering students, who generally think quite differently than students of mathematics. The objective is to emphasize mathematical methods and applications, rather than emphasizing general theorems and principles, for which the reader is referred to the literature. Vector analysis plays an important role in engineering, and is presented in terms of indicial notation, making use of the Einstein summation convention. This text differs from most texts in that symbolic vector notation is completely avoided, as suggested in the textbooks on tensor algebra and analysis written in German by Duschek and Hochreiner, in the 1960s. The defining properties of vector fields, the divergence and curl, are introduced in terms of fluid mechanics. The integral theorems of Gauss (the divergence theorem), Stokes, and Green are introduced also in the context of fluid mechanics. The final application of vector analysis consists of the introduction of non-Cartesian coordinate systems with straight axes, the formal definition of vectors and tensors. The stress and strain tensors are defined as an application. Partial differential equations of the first and second order are discussed. Two-dimensional linear partial differential equations of the second order are covered, emphasizing the three types of equation: hyperbolic, parabolic, and elliptic. The hyperbolic partial differential equations have two real characteristic directions, and writing the equations along these directions simplifies the solution process. The parabolic partial differential equations have two coinciding characteristics; this gives useful information regarding the character of the equation, but does not help in solving problems. The elliptic partial differential equations do not have real characteristics. In contrast to most texts, rather than abandoning the idea of using characteristics, here the complex characteristics are determined, and the differential equations are written along these characteristics. This leads to a generalized complex variable system, introduced by Wirtinger. The vector field is written in terms of a complex velocity, and the divergence and the curl of the vector field is written in complex form, reducing both equations to a single one. Complex variable methods are applied to elliptical problems in fluid mechanics, and linear elasticity. The techniques presented for solving parabolic problems are the Laplace transform and separation of variables, illustrated for problems of heat flow and soil mechanics. Hyperbolic problems of vibrating strings and bars, governed by the wave equation are solved by the method of characteristics as well as by Laplace transform. The method of characteristics for quasi-linear hyperbolic partial differential equations is illustrated for the case of a failing granular material, such as sand, underneath a strip footing. The Navier Stokes equations are derived and discussed in the final chapter as an illustration of a highly non-linear set of partial differential equations and the solutions are interpreted by illustrating the role of rotation (curl) in energy transfer of a fluid.
Fundamental Mechanics Of Fluids Fourth Edition
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Author : I.G. Currie
language : en
Publisher: CRC Press
Release Date : 2012-08-01
Fundamental Mechanics Of Fluids Fourth Edition written by I.G. Currie and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-01 with Technology & Engineering categories.
Fundamental Mechanics of Fluids, Fourth Edition addresses the need for an introductory text that focuses on the basics of fluid mechanics—before concentrating on specialized areas such as ideal-fluid flow and boundary-layer theory. Filling that void for both students and professionals working in different branches of engineering, this versatile instructional resource comprises five flexible, self-contained sections: Governing Equations deals with the derivation of the basic conservation laws, flow kinematics, and some basic theorems of fluid mechanics. Ideal-Fluid Flow covers two- and three-dimensional potential flows and surface waves. Viscous Flows of Incompressible Fluids discusses exact solutions, low-Reynolds-number approximations, boundary-layer theory, and buoyancy-driven flows. Compressible Flow of Inviscid Fluids addresses shockwaves as well as one- and multidimensional flows. Methods of Mathematical Analysis summarizes some commonly used analysis techniques. Additional appendices offer a synopsis of vectors, tensors, Fourier series, thermodynamics, and the governing equations in the common coordinate systems. The book identifies the phenomena associated with the various properties of compressible, viscous fluids in unsteady, three-dimensional flow situations. It provides techniques for solving specific types of fluid-flow problems, and it covers the derivation of the basic equations governing the laminar flow of Newtonian fluids, first assessing general situations and then shifting focus to more specific scenarios. The author illustrates the process of finding solutions to the governing equations. In the process, he reveals both the mathematical methodology and physical phenomena involved in each category of flow situation, which include ideal, viscous, and compressible fluids. This categorization enables a clear explanation of the different solution methods and the basis for the various physical consequences of fluid properties and flow characteristics. Armed with this new understanding, readers can then apply the appropriate equation results to deal with the particular circumstances of their own work.
Vectors And Tensors In Engineering And Physics
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Author : Donald Danielson
language : en
Publisher: Westview Press
Release Date : 2003-01-29
Vectors And Tensors In Engineering And Physics written by Donald Danielson and has been published by Westview Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-29 with Science categories.
Vectors and Tensors in Engineering and Physics develops the calculus of tensor fields and uses this mathematics to model the physical world. This new edition includes expanded derivations and solutions, and new applications. The book provides equations for predicting: the rotations of gyroscopes and other axisymmetric solids, derived from Euler's equations for the motion of rigid bodies; the temperature decays in quenched forgings, derived from the heat equation; the deformed shapes of twisted rods and bent beams, derived from the Navier equations of elasticity; the flow fields in cylindrical pipes, derived from the Navier-Stokes equations of fluid mechanics; the trajectories of celestial objects, derived from both Newton's and Einstein's theories of gravitation; the electromagnetic fields of stationary and moving charged particles, derived from Maxwell's equations; the stress in the skin when it is stretched, derived from the mechanics of curved membranes; the effects of motion and gravitation upon the times of clocks, derived from the special and general theories of relativity. The book also features over 100 illustrations, complete solutions to over 400 examples and problems, Cartesian components, general components, and components-free notations, lists of notations used by other authors, boxes to highlight key equations, historical notes, and an extensive bibliography.
Applications Of Tensor Analysis In Continuum Mechanics
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Author : Victor A Eremeyev
language : en
Publisher: World Scientific
Release Date : 2018-07-10
Applications Of Tensor Analysis In Continuum Mechanics written by Victor A Eremeyev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-10 with Technology & Engineering categories.
'A strong point of this book is its coverage of tensor theory, which is herein deemed both more readable and more substantial than many other historic continuum mechanics books. The book is self-contained. It serves admirably as a reference resource on fundamental principles and equations of tensor mathematics applied to continuum mechanics. Exercises and problem sets are useful for teaching … The book is highly recommended as both a graduate textbook and a reference work for students and more senior researchers involved in theoretical and mathematical modelling of continuum mechanics of materials. Key concepts are well described in the text and are supplemented by informative exercises and problem sets with solutions, and comprehensive Appendices provide important equations for ease of reference.'Contemporary PhysicsA tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems. The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. These rules are relatively simple and easily grasped by any engineering student familiar with matrix operators in linear algebra. More complex problems arise when one considers the tensor fields that describe continuum bodies. In this case general curvilinear coordinates become necessary. The principal basis of a curvilinear system is constructed as a set of vectors tangent to the coordinate lines. Another basis, called the dual basis, is also constructed in a special manner. The existence of these two bases is responsible for the mysterious covariant and contravariant terminology encountered in tensor discussions.This book provides a clear, concise, and self-contained treatment of tensors and tensor fields. It covers the foundations of linear elasticity, shell theory, and generalized continuum media, offers hints, answers, and full solutions for many of the problems and exercises, and Includes a handbook-style summary of important tensor formulas.The book can be useful for beginners who are interested in the basics of tensor calculus. It also can be used by experienced readers who seek a comprehensive review on applications of the tensor calculus in mechanics.
Fundamental Directions In Mathematical Fluid Mechanics
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Author : Giovanni P. Galdi
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Fundamental Directions In Mathematical Fluid Mechanics written by Giovanni P. Galdi and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume consists of six articles, each treating an important topic in the theory ofthe Navier-Stokes equations, at the research level. Some of the articles are mainly expository, putting together, in a unified setting, the results of recent research papers and conference lectures. Several other articles are devoted mainly to new results, but present them within a wider context and with a fuller exposition than is usual for journals. The plan to publish these articles as a book began with the lecture notes for the short courses of G.P. Galdi and R. Rannacher, given at the beginning of the International Workshop on Theoretical and Numerical Fluid Dynamics, held in Vancouver, Canada, July 27 to August 2, 1996. A renewed energy for this project came with the founding of the Journal of Mathematical Fluid Mechanics, by G.P. Galdi, J. Heywood, and R. Rannacher, in 1998. At that time it was decided that this volume should be published in association with the journal, and expanded to include articles by J. Heywood and W. Nagata, J. Heywood and M. Padula, and P. Gervasio, A. Quarteroni and F. Saleri. The original lecture notes were also revised and updated.
Handbook Of Computational Fluid Mechanics
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Author :
language : en
Publisher: Elsevier
Release Date : 1996-03-25
Handbook Of Computational Fluid Mechanics written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-03-25 with Science categories.
This handbook covers computational fluid dynamics from fundamentals to applications. This text provides a well documented critical survey of numerical methods for fluid mechanics, and gives a state-of-the-art description of computational fluid mechanics, considering numerical analysis, computer technology, and visualization tools. The chapters in this book are invaluable tools for reaching a deeper understanding of the problems associated with the calculation of fluid motion in various situations: inviscid and viscous, incompressible and compressible, steady and unsteady, laminar and turbulent flows, as well as simple and complex geometries.Each chapter includes a related bibliographyCovers fundamentals and applicationsProvides a deeper understanding of the problems associated with the calculation of fluid motion