Fundamental Mechanics of Fluids, 4/e (Hardcover)

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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.

Table Of Contents

Part I: Governing Equations

Basic Conservation Laws

Statistical and Continuum Methods

Eulerian and Lagrangian Coordinates

Material Derivative

Control Volumes

Reynolds’ Transport Theorem

Conservation of Mass

Conservation of Momentum

Conservation of Energy

Discussion of Conservation Equations

Rotation and Rate of Shear

Constitutive Equations

Viscosity Coefficients

Navier–Stokes Equations

Energy Equation

Governing Equations for Newtonian Fluids

Boundary Conditions

Flow Kinematics

Flow Lines

Circulation and Vorticity

Stream Tubes and Vortex Tubes

Kinematics of Vortex Lines

Special Forms of the Governing Equations

Kelvin’s Theorem

Bernoulli Equation

Crocco’s Equation

Vorticity Equation

Part II: Ideal-Fluid Flow

Two-Dimensional Potential Flows

Stream Function

Complex Potential and Complex Velocity

Uniform Flows

Source, Sink, and Vortex Flows

Flow in Sector

Flow around Sharp Edge

Flow due to Doublet

Circular Cylinder without Circulation

Circular Cylinder with Circulation

Blasius Integral Laws

Force and Moment on Circular Cylinder

Conformal Transformations

Joukowski Transformation

Flow around Ellipses

Kutta Condition and Flat-Plate Airfoil

Symmetrical Joukowski Airfoil

Circular-Arc Airfoil

Joukowski Airfoil

Schwarz–Christoffel Transformation

Source in Channel

Flow through Aperture

Flow Past Vertical Flat Plate

Three-Dimensional Potential Flows

Velocity Potential

Stokes’ Stream Function

Solution of Potential Equation

Uniform Flow

Source and Sink

Flow due to Doublet

Flow near Blunt Nose

Flow around Sphere

Line-Distributed Source

Sphere in Flow Field of Source

Rankine Solids

D’Alembert’s Paradox

Forces Induced by Singularities

Kinetic Energy of Moving Fluid

Apparent Mass

Surface Waves

General Surface-Wave Problem

Small-Amplitude Plane Waves

Propagation of Surface Waves

Effect of Surface Tension

Shallow-Liquid Waves of Arbitrary Form

Complex Potential for Traveling Waves

Particle Paths for Traveling Waves

Standing Waves

Particle Paths for Standing Waves

Waves in Rectangular Vessels

Waves in Cylindrical Vessels

Propagation of Waves at Interface

Part III: Viscous Flows of Incompressible Fluids

Exact Solutions

Couette Flow

Poiseuille Flow

Flow between Rotating Cylinders

Stokes’ First Problem

Stokes’ Second Problem

Pulsating Flow between Parallel Surfaces

Stagnation-Point Flow

Flow in Convergent and Divergent Channels

Flow over Porous Wall

Low Reynolds Number Solutions

Stokes Approximation

Uniform Flow

Doublet

Rotlet

Stokeslet

Rotating Sphere in Fluid

Uniform Flow Past Sphere

Uniform Flow Past Circular Cylinder

Oseen Approximation

Boundary Layers

Boundary-Layer Thicknesses

Boundary-Layer Equations

Blasius Solution

Falkner–Skan Solutions

Flow over a Wedge

Stagnation-Point Flow

Flow in Convergent Channel

Approximate Solution for Flat Surface

General Momentum Integral

Ka'rma'n–Pohlhausen Approximation

Boundary-Layer Separation

Stability of Boundary Layers

Buoyancy-Driven Flows

Boussinesq Approximation

Thermal Convection

Boundary-Layer Approximations

Vertical Isothermal Surface

Line Source of Heat

Point Source of Heat

Stability of Horizontal Layers

Part IV: Compressible Flow of Inviscid Fluids

Shock Waves

Propagation of Infinitesimal Disturbances

Propagation of Finite Disturbances

Rankine-Hugoniot Equations

Conditions for Normal Shock Waves

Normal-Shock-Wave Equations

Oblique Shock Waves

One-Dimensional Flows

Weak Waves

Weak Shock Tubes

Wall Reflection of Waves

Reflection and Refraction at Interface

Piston Problem

Finite-Strength Shock Tubes

Nonadiabatic Flows

Isentropic-Flow Relations

Flow through Nozzles

Multidimensional Flows

Irrotational Motion

Janzen–Rayleigh Expansion

Small-Perturbation Theory

Pressure Coefficient

Flow over Wave-Shaped Wall

Prandtl–Glauert Rule for Subsonic Flow

Ackeret’s Theory for Supersonic Flows

Prandtl–Meyer Flow

Part V: Methods of Mathematical Analysis

Some Useful Methods of Analysis

Fourier Series

Complex Variables

Separation of Variable Solutions

Similarity Solutions

Group Invariance Methods

Appendix A: Vector Analysis

Vector Identities

Integral Theorems

Orthogonal Curvilinear Coordinates

Appendix B: Tensors

Notation and Definition

Tensor Algebra

Tensor Operations

Isotropic Tensors

Integral Theorems

Appendix C: Governing Equations

Cartesian Coordinates

Cylindrical Coordinates

Spherical Coordinates

Appendix D: Fourier Series

Appendix E: Thermodynamics

Zeroth Law

First Law

Equations of State

Enthalpy

Specific Heats

Adiabatic, Reversible Processes

Entropy

Second Law

Canonical Equations of State

Reciprocity Relations

《流體力學基礎》第四版針對流體力學基礎知識的需求，提供了一本入門教材，先著重介紹基本的流體力學概念，再深入探討理想流體流動和邊界層理論等專業領域。這本教材填補了工程學不同分支的學生和專業人士的需求，包含五個靈活、獨立的部分：

* 控制方程式部分介紹了基本守恆定律的推導、流動運動學和一些基本的流體力學定理。
* 理想流體流動部分涵蓋了二維和三維的位勢流和表面波動。
* 不可壓縮流體黏性流動部分討論了精確解、低雷諾數近似、邊界層理論和浮力驅動流動。
* 不可壓縮流體可壓縮流動部分涵蓋了衝擊波以及一維和多維流動。
* 數學分析方法部分總結了一些常用的分析技巧。附錄還提供了向量、張量、傅立葉級數、熱力學和常見坐標系統中的控制方程式的概要。

本書確定了與不可壓縮、黏性流體在非穩定、三維流動情況下相關的現象。它提供了解決特定類型流體流動問題的技巧，並涵蓋了基本的牛頓流體層流方程的推導，首先評估一般情況，然後專注於更具體的情景。

作者以實例說明了尋找控制方程式解的過程。在此過程中，他揭示了每個流動情況中涉及的數學方法和物理現象，包括理想流體、黏性流體和可壓縮流體。這種分類使得能夠清晰解釋不同解決方法和流體性質以及流動特性的各種物理結果的基礎。讀者在獲得這種新的理解後，可以將適當的方程結果應用於處理自己工作的特定情況。

目錄：

第一部分：控制方程式

基本守恆定律

統計和連續方法

歐拉和拉格朗日座標

物質導數

控制體

雷諾運輸定理

質量守恆

動量守恆

能量守恆

守恆方程式討論

旋轉和剪切速率

本構方程式

黏滯係數

納維爾-斯托克斯方程式

能量方程式

牛頓流體的控制方程式

邊界條件

流動運動學

流線

環流和渦度

流管和渦管

渦線運動學

控制方程式的特殊形式

開爾文定理

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