Calculus I & II, Linear Algebra, Physics I & II

Fundamental and applied knowledge of the laws that determine the fluid motion and their application to problems of interest in engineering: conservation laws for mass, momentum and energy (integral and differential form), dimensional analysis and simplifications of the general equations

CB2: Students are able to apply their knowledge to their work or vocation in a professional manner and possess the competences usually demonstrated through the development and defence of arguments and problem solving within their field of study. CB5: Students will have developed the learning skills necessary to undertake further study with a high degree of autonomy. CG5: Ability to carry out projection activities, technical management, expert appraisal, drafting of reports, opinions, and technical advice in tasks related to Aeronautical Technical Engineering, the exercise of genuinely aerospace technical functions and positions. CG9: Ability to analyse and solve aerospace problems in new or unknown environments, within broad and complex contexts, integrated in multidisciplinary and international work teams. CG10: Ability to use computational and experimental tools for the analysis and quantification of engineering problems. CE.CRA10: Adequate knowledge and application to Engineering of: The concepts and laws governing energy transfer processes, fluid motion, heat transfer mechanisms and matter change and their role in the analysis of the main aerospace propulsion systems. CE.CRA12: Adequate knowledge and application to engineering of: The fundamentals of fluid mechanics; the basic principles of flight control and automation; the main physical and mechanical characteristics and properties of materials. CE.CRA13: Applied knowledge of: the science and technology of materials; mechanics and thermodynamics; fluid mechanics; aerodynamics and flight mechanics; navigation and air traffic systems; aerospace technology; theory of structures; air transport; economics and production; projects; environmental impact. RA1: Have basic knowledge and understanding of mathematics, basic sciences, and engineering within the aerospace field, including: behaviour of structures; thermodynamic cycles and fluid mechanics; the air navigation system, air traffic, and coordination with other means of transport; aerodynamic forces; flight dynamics; materials for aerospace use; manufacturing processes; airport infrastructures and buildings. In addition to a specific knowledge and understanding of the specific aircraft and aero-engine technologies in each of the subjects included in this degree. RA2: Be able to identify aerospace engineering problems, recognise specifications, collect and interpret data and information, establish different resolution methods and select the most appropriate among the available alternatives. RA3: Be able to carry out designs in the field of aerospace vehicles, propulsion systems, navigation and air traffic control, airport infrastructures, or equipment and materials for aerospace use, which comply with the required specifications, collaborating with other engineers and graduates. RA4: Graduates will be able to carry out initial research methods approaches commensurate with their level of knowledge involving literature searches, design and execution of experiments, data interpretation, selection of the best proposal and computer simulation. RA6: Have the necessary skills for the practice of engineering in today's society.

1. Introduction to Fluid Mechanics 1.1. Solids, liquids and gases. 1.2. The fluid as a continuum: Fluid particles. 1.3. Density, velocity and internal energy. 1.4. Local thermodynamic equilibrium. 1.5. Equations of state. 2. Flow kinematics 2.1 Coordinate systems 2.2 Eulerian and Lagrangian descriptions. Uniform flow. Steady flow. Stagnation points. 2.3 Trajectories. Paths. Fluid lines, Fluid surface, Fluid Volume. 2.4 Streamlines, stream surface and stream tubes 2.5 Material derivative. Acceleration 2.6 Circulation and vorticity. 2.7 Irrotational flow. Velocity Potential 2.8 Stream function 2.9 Local flow deformation. Strain-rate tensor 2.10 Convective flow 2.11 Reynolds transport theorem. 3. Conservation Laws 3.1. Continuity equation in integral form 3.2 Volume and surface forces 3.3 Stress tensor. Navier-Poisson law 3.4 Forces and moments on submerged bodies 3.5 Momentum equation in integral form 3.6 Angular momentum equation in integral form 3.7 Heat conduction 3.8 Energy equation in integral form. Different forms of the energy equation. 4. Conservation equations in differential form: Navier-Stokes equations. 4.1 Continuity equation 4.2 Momentum equation 4.3 Energy equation. Internal energy and kinetic energy equations. Enthalpy and entropy equations. 4.4 Initial and boundary conditions 4.5 Bernoulli's equation. 5. Fluid statics 5.1 Equilibrium equations 5.2 Hydrostatics 5.3 Forces and moments on submerged bodies. Archimedes' Principle. 5.4 The standard atmosphere 6. Dimensional analysis 6.1 Dimensions of a physical magnitude 6.2 Physical quantities with independent dimensions 6.3 The Pi theorem 6.4 Nondimensionalization of the Navier-Stokes equations; Dimensionless numbers in Fluid Mechanics 6.5 Physical similarity. Partial similarity. Applications. 7. Viscous flow 7.1 Uni-directional viscous flow in channels and pipes: Poiseuille and Couette flows 7.2 Uni-directional unsteady flows: Rayleigh's problem and Stokes' flow 7.3 Flows dominated by viscosity in ducts and channels of slowly varying cross section 7.4 The pipe entrance region 7.5 Introduction to hydrodynamic lubrication. The wedge effect.

The methodology will combine lecture classes for presentation of the fundamentals with problem solving sessions. 3 of the laboratory sessions, to take place in the computer room, are designed to provide a brief introduction to CFD, to enable students to use FLUENT for solving realistic flow problems. One of the lab sessions will consist of hands-on work in the lab to take measures in a real problem and then use dimensional analysis.