- All the courses in mathematics (calculus, algebra, etc.) - Engineering fluid mechanics

By the end of this subject, students will be able to have: 1. A systematic understanding of the key aspects and concepts of hydraulic machines and systems. 2. The ability to apply their knowledge and understanding to identify, formulate and solve problems of hydraulic machines and systems using established methods. 3. The ability to select and apply relevant analytic and modelling methods in hydraulic machines and systems. 4. An understanding of design methodologies in fluid mechancis, and an ability to use them. 5. The ability to combine theory and practice to solve problem of hydraulics. 6. An understanding of applicable techniques and methods in hydraulic machines and systems, and of their limitations. 7. Function effectively as an individual and as a member of a team.

This is an eminently practical course, so the student must master the necessary fundamental knowledges at the time on enrollment. CHAPTER 1: Steady flow of liquids in ducts 1.1 Primary head losses. Colebrook correlation and Moody¿s chart. 1.2 Non-circular cross-section ducts. Hydraulic diameter. 1.3 Localized head losses: Valves, Elbows, curves, expansions, contractions, etc. 1.4 Coupling of turbomachinery to hydraulic facilities. CHAPTER 2: Steady flow of liquids in pipe networks. 2.1 Pipes in series and in parallel. 2.2 Analysis of branched ducts: the three-reservoirs problem. 2.3 Analysis of closed-loop pipe networks. Matrix algorithm and its numerical implementation. CHAPTER 3: Unsteady phenomena in pipe flow. 3.1 Theory of unsteady incompressible flow in ducts. 3.2 Characteristic acceleration and discharge times. Quasi-steady flow. 3.3 Order-of-magnitude analysis of characteristic variables in unsteady pipenetworks flow. Non-dimensionalization of the equations. 3.4 Applications. Surge tanks. 3.5 Compressibility effects. Basic theory of water hammer. Reflection and transmission of waves. Applications. CHAPTER 4: Introduction to turbomachinery. 4.1 Definitions. Classification of incompressible fluid machines. 4.2 Characteristic curves of pumps ad turbines. 4.3 Cavitation in turbomachinery. 4.4 Similarity in pumps. 4.5 Similarity in turbines. 4.6 Coupling of pumps and turbines to a hydraulic network.

The methodology will include: (1) Lectures, where the basic knowledges will be exposed. (2) Resolution of problems. (3) Resolution of problems by the student, that will be useful to self-assess his/her knowledge and develop the necessary skills. (4) The students will attend to the lab sessions and elaborate the lab reports.