Fluid Mechanics: Analytical Methods

ISBN-13: 9781848219519 / Angielski / Twarda / 2017 / 304 str.

Michel LeDoux; Abdelkhalak El Hami

Opis

The book aims to provide an efficient methodology of solving a fluid mechanics problem. It aims to meet different objectives of the student, the future engineer or scientist. Using simple sizing calculations, and more advanced analytical calculations, the book covers all the essential numerical approaches for solving complex practical problems.

Spis treści

Preface ix

Chapter 1. Mechanics and Fluid  1

1.1. Introduction  1

1.1.1. Mechanics: what to remember  1

1.1.2. Momentum theorem 4

1.1.3. Kinetic energy theorem  5

1.1.4. Forces deriving from a potential 6

1.1.5. Conserving the energy of a material point 8

1.2. The fluid state   9

1.2.1. Fluid properties  9

1.2.2. Forces applied to a fluid 12

1.3. How to broach a question in fluid mechanics  22

1.3.1. The different approaches of fluid mechanics  22

1.3.2. Strategies for arriving at a reasoned solution  23

1.4. Conclusion 25

Chapter 2. Immobile Fluid  27

2.1. Introduction  27

2.1.1. The fundamental theorem of fluid statics  27

2.2. Determining the interface position and related questions 30

2.2.1. Fluid statics. Incompressible fluids subject to gravity 30

2.2.2. Case of volume forces deriving from a potential  43

2.2.3. Case for compressible fluids 51

2.3. Calculating the thrusts 57

2.3.1. Methods  57

2.3.2. Thrusts on bodies that are totally immersed in incompressible fluids 58

2.3.3. Calculating the thrust on a wall 79

Chapter 3. A Description of Flows 87

3.1. Introduction  87

3.2. The description of a fluid flow  88

3.2.1. The Eulerian and Lagrangian description  88

3.2.2. Kinematic elements  91

3.2. A first principle of physics: the principle of continuity 96

3.2.1. The principle of continuity  96

3.3. Notions and recalls on potential flows  102

3.3.1. Definition 102

3.3.2. Determination 102

3.3.3. Determining streamlines 104

3.3.4. Curl of the velocity  104

3.4. Example of kinematic calculations  105

Chapter 4. Dynamics of Inviscid Fluids  127

4.1. Introduction  127

4.2. The Bernoulli theorem: proof 127

4.2.1. What to retain 133

4.2.2. Energetic interpretation of the Bernoulli theorem 134

4.2.3. Physical interpretation of the Bernoulli theorem  135

4.2.4. Constant energy flows 135

4.3. Applications of the Bernoulli theorem  136

4.3.1. Methodology for the resolution of a problem using the Bernoulli theorem 136

4.3.2. Determining an applicate 145

4.3.3. Draining and filling  150

4.3.4. Mobile reference frame  157

4.3.5. Time–dependent filling  168

4.4. Draining of the ballasts  177

4.5. Synthetic problems  179

Chapter 5. Viscous Fluid Flows: Calculating Head Losses  197

5.1. Introduction  197

5.2. The notion of head: generalized heads  198

5.3. Practical calculation of a head loss  200

5.3.1. Introduction  200

5.3.2. Linear head losses 201

5.3.3. Singular loss of head 203

5.4. Circuit calculations  205

Chapter 6. Calculation of Thrust and Propulsion  235

6.1. Introduction  235

6.2. Euler s theorem and proof  235

6.2.1. Euler s first theorem and proof 236

6.3. Thrust of a jet propulsion system, and propulsive efficiency  240

6.3.1. Calculation of the thrust of an airplane engine   240

6.3.2. Calculation of the propulsive efficiency  244

6.3.3. Calculation of the thrust of a rocket engine 246

6.3.4. Some applications of Euler s theorem to jet propulsion 247

6.4. Thrust exerted by a jet on a fixed wall  263

6.4.1. Calculation of the thrust applied to a wall by a jet 263

6.4.2. Jet impacting on a wall  266

6.5. Other applications for Euler s theorems 272

6.5.1. Application of Euler s theorem to a head loss calculation 272

6.5.2. A case for the application of Euler s second theorem 277

Bibliography 283

Index 285