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Hydrodynamics: Examples and Problems

978-1-56700-159-4 (Print)
978-1-56700-381-9 (Online)

Hydrodynamics: Examples and Problems

Dmitri V. Alexandrov
Urals State University, Ekaterinburg, Russian Federation

Yu. A. Buyevich
CRSS, University of California, Santa Barbara, USA

S. V. Zakharov
Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia


There are more than 200 examples and problems supplemented by answers and solutions in this book. In this textbook, the authors primarily propose the problems, the physical content of which is rather transparent, and the process of solving allows the reader to see all the beauty of hydrodynamics. The authors have deliberately excluded problems whose solution might require rigorous mathematical proofs of different theorems and statements. The useful and unique publication.

341 pages, © 2001

Table of Contents:

1. Tensor Analysis
1.1 Contravariant and Covariant Components of Tensors
1.2 Transformation of Components of a Vector
1.2.1 Definition of a Tensor
1.2.2 Addition of Tensors
1.2.3 Raising and Lowering of Indices Rule
1.2.4 Contraction of Tensors
1.3 Orthogonal Curvilinear Coordinates
1.4 Covariant Derivative
1.5 Operators in Curvilinear Coordinates
1.6 Problems
2. Dimensional Analysis
2.1 Introduction
2.2 The π Theorem
2.3 Problems
3. Self-Similar Solutions
3.1 Introduction
3.2 Classification of Self-Similar Solutions
3.3 Running Waves
3.4 Linear Processes
3.5 Noninear Processes
3.6 Problems
4. Inviscid Flows
4.1 Hydrostatics
4.2 Bernoulli's Equation
4.3 Plane Potential Flow of an Inviscid Incompressible Fluid: Method I
4.4 Potential Inviscid Incompressible Flows: Sloving Problems by Means of Separation of Variables (Method II)
4.5 Waves
4.5.1 Gravitational Waves
4.5.2 Capillary Waves
4.5.3 Standing Waves in Vessel
4.6 Some Cases of Fluid Motion
4.6.1 Inviscid Fluids of Constant Density
4.6.2 Inviscid Fluids of Variable Density
4.7 Problems
5. Viscous Fluids
5.1 Exact Solutions of Stationary Navier-Stokes Equations for Homogeneous, Viscous, Incompressible Fluids
5.2 Motion of Homogeneous Viscous Incompressible Fluids at Small Reynolds Number: The Stokes Method
5.3 Nonstationary Viscous Incompressible Flow
5.4 Low Reynolds Number Flow of Viscous Fluids: The Oseen Method
5.5 Boundary Layers
5.5.1 Governing Equations
5.5.2 The Karman Integral Relation
5.5.3 Approximate Method Solving Boundary Layer Equations
5.5.4 Approximate Boundary Layer Equations
5.5.5 Thin Laminar Jets
5.5.6 Application of the Boundary Layer Theory to the Problem of Damped Rotation of a Body in an Airflow
5.5.7 Boundary Layer Near a Rotation Body
5.6 Evolution of Laminar Motion
5.7 Problems
Solutions and Answers to Selected Problems