Michel Ledoux is Professeur des universités. He was formerly Vice-President for Research at the University of Rouen in France, then Regional Delegate for the Ministry of Education in the region of High Normandy for Research and Technology. He is now retired from University, but is Counselor at the Conservatoire de Arts et Métiers in Normandy and still teaches physics to apprentice-engineers (Cnam and ITII). He was involved in reacting flows and spray systems research.Abdelkhalak El Hami is Professeur des universités at the Institut National des Sciences Appliquées (INSA-Rouen) in France and is in charge of the Normandy Conservatoire National des Arts et Metiers (CNAM) Chair of Mechanics, as well as several European pedagogical projects. He is an expert in fluid-structure interaction studies and reliability.

• Preface ixChapter 1. Mechanics and Fluid 11.1. Introduction 11.1.1. Mechanics: what to remember 11.1.2. Momentum theorem 41.1.3. Kinetic energy theorem 51.1.4. Forces deriving from a potential 61.1.5. Conserving the energy of a material point 81.2. The “fluid state” 91.2.1. Fluid properties 91.2.2. Forces applied to a fluid 121.3. How to broach a question in fluid mechanics 221.3.1. The different approaches of fluid mechanics 221.3.2. Strategies for arriving at a reasoned solution 231.4. Conclusion 25Chapter 2. Immobile Fluid 272.1. Introduction 272.1.1. The fundamental theorem of fluid statics 272.2. Determining the interface position and related questions 302.2.1. Fluid statics. Incompressible fluids subject to gravity 302.2.2. Case of volume forces deriving from a potential 432.2.3. Case for compressible fluids 512.3. Calculating the thrusts 572.3.1. Methods 572.3.2. Thrusts on bodies that are totally immersed in incompressible fluids 582.3.3. Calculating the thrust on a wall 79Chapter 3. A Description of Flows 873.1. Introduction 873.2. The description of a fluid flow 883.2.1. The Eulerian and Lagrangian description 883.2.2. Kinematic elements 913.2. A first principle of physics: the principle of continuity 963.2.1. The principle of continuity 963.3. Notions and recalls on potential flows 1023.3.1. Definition 1023.3.2. Determination 1023.3.3. Determining streamlines 1043.3.4. Curl of the velocity 1043.4. Example of kinematic calculations 105Chapter 4. Dynamics of Inviscid Fluids 1274.1. Introduction 1274.2. The Bernoulli theorem: proof 1274.2.1. What to retain 1334.2.2. Energetic interpretation of the Bernoulli theorem 1344.2.3. Physical interpretation of the Bernoulli theorem 1354.2.4. “Constant energy” flows 1354.3. Applications of the Bernoulli theorem 1364.3.1. Methodology for the resolution of a problem using the Bernoulli theorem 1364.3.2. Determining an applicate 1454.3.3. Draining and filling 1504.3.4. Mobile reference frame 1574.3.5. Time-dependent filling 1684.4. Draining of the ballasts 1774.5. Synthetic problems 179Chapter 5. Viscous Fluid Flows: Calculating Head Losses 1975.1. Introduction 1975.2. The notion of head: generalized heads 1985.3. Practical calculation of a head loss 2005.3.1. Introduction 2005.3.2. Linear head losses 2015.3.3. Singular loss of head 2035.4. Circuit calculations 205Chapter 6. Calculation of Thrust and Propulsion 2356.1. Introduction 2356.2. Euler’s theorem and proof 2356.2.1. Euler’s first theorem and proof 2366.3. Thrust of a jet propulsion system, and propulsive efficiency 2406.3.1. Calculation of the thrust of an “airplane engine” 2406.3.2. Calculation of the propulsive efficiency 2446.3.3. Calculation of the thrust of a rocket engine 2466.3.4. Some applications of Euler’s theorem to jet propulsion 2476.4. Thrust exerted by a jet on a fixed wall 2636.4.1. Calculation of the thrust applied to a wall by a jet 2636.4.2. Jet impacting on a wall 2666.5. Other applications for Euler’s theorems 2726.5.1. Application of Euler’s theorem to a head loss calculation 2726.5.2. A case for the application of Euler’s second theorem 277Bibliography 283Index 285

Michel Ledoux is Professeur des universités. He was formerly Vice-President for Research at the University of Rouen in France, then Regional Delegate for the Ministry of Education in the region of High Normandy for Research and Technology. He is now retired from University, but is Counselor at the Conservatoire de Arts et Métiers in Normandy and still teaches physics to apprentice-engineers (Cnam and ITII). He was involved in reacting flows and spray systems research.Abdelkhalak El Hami is Professeur des universités at the Institut National des Sciences Appliquées (INSA-Rouen) in France and is in charge of the Normandy Conservatoire National des Arts et Metiers (CNAM) Chair of Mechanics, as well as several European pedagogical projects. He is an expert in fluid-structure interaction studies and reliability.

• Preface ixChapter 1. Mechanics and Fluid 11.1. Introduction 11.1.1. Mechanics: what to remember 11.1.2. Momentum theorem 41.1.3. Kinetic energy theorem 51.1.4. Forces deriving from a potential 61.1.5. Conserving the energy of a material point 81.2. The “fluid state” 91.2.1. Fluid properties 91.2.2. Forces applied to a fluid 121.3. How to broach a question in fluid mechanics 221.3.1. The different approaches of fluid mechanics 221.3.2. Strategies for arriving at a reasoned solution 231.4. Conclusion 25Chapter 2. Immobile Fluid 272.1. Introduction 272.1.1. The fundamental theorem of fluid statics 272.2. Determining the interface position and related questions 302.2.1. Fluid statics. Incompressible fluids subject to gravity 302.2.2. Case of volume forces deriving from a potential 432.2.3. Case for compressible fluids 512.3. Calculating the thrusts 572.3.1. Methods 572.3.2. Thrusts on bodies that are totally immersed in incompressible fluids 582.3.3. Calculating the thrust on a wall 79Chapter 3. A Description of Flows 873.1. Introduction 873.2. The description of a fluid flow 883.2.1. The Eulerian and Lagrangian description 883.2.2. Kinematic elements 913.2. A first principle of physics: the principle of continuity 963.2.1. The principle of continuity 963.3. Notions and recalls on potential flows 1023.3.1. Definition 1023.3.2. Determination 1023.3.3. Determining streamlines 1043.3.4. Curl of the velocity 1043.4. Example of kinematic calculations 105Chapter 4. Dynamics of Inviscid Fluids 1274.1. Introduction 1274.2. The Bernoulli theorem: proof 1274.2.1. What to retain 1334.2.2. Energetic interpretation of the Bernoulli theorem 1344.2.3. Physical interpretation of the Bernoulli theorem 1354.2.4. “Constant energy” flows 1354.3. Applications of the Bernoulli theorem 1364.3.1. Methodology for the resolution of a problem using the Bernoulli theorem 1364.3.2. Determining an applicate 1454.3.3. Draining and filling 1504.3.4. Mobile reference frame 1574.3.5. Time-dependent filling 1684.4. Draining of the ballasts 1774.5. Synthetic problems 179Chapter 5. Viscous Fluid Flows: Calculating Head Losses 1975.1. Introduction 1975.2. The notion of head: generalized heads 1985.3. Practical calculation of a head loss 2005.3.1. Introduction 2005.3.2. Linear head losses 2015.3.3. Singular loss of head 2035.4. Circuit calculations 205Chapter 6. Calculation of Thrust and Propulsion 2356.1. Introduction 2356.2. Euler’s theorem and proof 2356.2.1. Euler’s first theorem and proof 2366.3. Thrust of a jet propulsion system, and propulsive efficiency 2406.3.1. Calculation of the thrust of an “airplane engine” 2406.3.2. Calculation of the propulsive efficiency 2446.3.3. Calculation of the thrust of a rocket engine 2466.3.4. Some applications of Euler’s theorem to jet propulsion 2476.4. Thrust exerted by a jet on a fixed wall 2636.4.1. Calculation of the thrust applied to a wall by a jet 2636.4.2. Jet impacting on a wall 2666.5. Other applications for Euler’s theorems 2726.5.1. Application of Euler’s theorem to a head loss calculation 2726.5.2. A case for the application of Euler’s second theorem 277Bibliography 283Index 285