Classical Fluid Mechanics

Michael Belevich

• Publisher: Bentham Science Publishers
• Year: 2017
• Print ISBN: 9781681084107
• eBook ISBN: 9781681084091
• Topic: Physical Sciences
• Subtopic: Aerodynamics

This textbook primarily explains the construction of the classical fluid model to readers in a holistic manner. Secondly, the book also explains some possible modifications of the classical fluid model which either make the model applicable in some special cases (viscous or turbulent fluids) or simplify it in accordance with the specific mechanical properties (hydrostatics, two-dimensional flows, boundary layers, etc.). The book explains theoretical concepts in two parts. The first part is dedicated to the derivation of the classical model of the perfect fluid. The second part of the book covers important modifications to the fluid model which account for calculations of momentum, force and the laws of energy conservation. Concepts in this section include the redefinition of the stress tensor in cases of viscous or turbulent flows and laminar and turbulent boundary layers. The text is supplemented by appropriate exercises and problems which may be used in practical classes. These additions serve to teach students how to work with complex systems governed by differential equations. Classical Fluid Mechanics is an ideal textbook for students undertaking semester courses on fluid physics and mechanics in undergraduate degree programs.

Part I

Model of continuum

A scientific law is a statement … possessing such attributes: 1) it is true only under certain conditions; 2) under these conditions, it is true always and everywhere without any exceptions…; 3) conditions under which this statement is true, are never realized in fact fully, but only partially and approximately. Therefore, it’s impossible to say literally that scientific laws are found in the study of reality (are discovered). They are devised (are invented) based on the study of experimental data in such a way that they then may be used to obtain new judgments of given judgments on the reality (including, for prediction purely logical way). Scientific laws themselves can not be verified and can not be refuted by experience. They can be justified or not, depending on how well or poorly they perform the above-mentioned role.

A. Zinoviev
Yawning Heights

Bodies and Their Characteristics

Michael Belevich

St.Petersburg, Russia

Abstract

This introductory chapter tries to explain what we are going to do, what do notions such as fluid and a model of a physical phenomenon mean, what for, such models are developed, and what features of a phenomenon a model should be necessarily able to describe and so on.

Keywords: Body, Body configuration, Coordinate basis, Event, Fluid, Force, Frame of reference, Mass, Model, Motion, Place, Space-time continuum, System of coordinates, Trajectory, World-line.

1.1. INTRODUCTION

All natural-science disciplines have one and the same way of development: from gathering of facts, their classification, towards formalization of an object of research and its modeling. Fluid mechanics has attained a considerable progress in this regard. A lot of information has been collected over past centuries about properties and behavior of those objects which we now call gases, liquids and solids. Common features and differences of objects of study have been revealed as a result of systematization of this data. Basic properties of studied phenomena, and laws which these properties obey have been understood and formulated. Mathematical models which allow one to describe observations and predict changes of the form, position in the space and some other properties of simulated objects¹ have been constructed. These models essentially are the subject of the present course.

Our task is to examine hypotheses which define objects of study, axioms², underlying the described models, and the consequences arising out of these hypotheses and axioms. We emphasize again: the subject of the course are mathematical models of fluid dynamics. It is necessary to understand, th...

Table of contents

• Welcome
• Table of Contents
• Title Page
• BENTHAM SCIENCE PUBLISHERS LTD.
• FOREWORD
• PREFACE
• Part I Model of continuum
• Bodies and Their Characteristics
• Basic Hypotheses and Laws
• Rates of Change of Characteristics of Continuum
• Minimum Information About Tensors
• Deformation
• The Continuity Equation
• Fluid Dynamics
• Energy
• Part II Applications of the fluid model
• Perfect Fluid
• Incompressible Perfect Fluid
• Viscous Fluid
• Related Topics
• Turbulent Fluid
• Boundary Layers
• Part III Supplement
• Fluid Mechanics from an Observer’s Viewpoint
• Exercises
• List of Notations
• Text Books for Further Reading
• References