Calculus I and II Linear algebra Differential equations Physics I, II, and III Biomechanics of continuum media I (solid mechanics)

- The students must become familiar with the basic concepts of Fluid Mechanics: conservation laws, dimensional analysis, simplification of the general equations, etc. - The students must become fluent in the usage of the mathematical tools commonly used in fluid mechanics: partial differential equations, usage of different coordinate systems, surface and volume integrals, complex variable, etc.

K3. To know the fundamentals of basic scientific and technical subjects in the field of biomedical engineering, which enable to learn new methods and technologies, as well as provide great versatility to adapt to new situations. S3. To analyze and synthesize basic problems related to bioengineering and biomedical sciences, solving them with initiative, appropriate decision making and creativity and communicating solutions efficiently, including social, ethical, health and safety, environmental, economic and industrial implications. S4. Draw up a scientific-technical project in the field of Bioengineering with the appropriate methodology and in accordance with the regulations in force and with respect for ethical principles. S5. To analyse scientific and technical information for decision-making in the field of biomedical engineering by keeping abreast of new developments S7. Solve those problems characteristic of fluid and solid mechanics and the theory of transport of momentum, heat, mass, etc. in continuous media in biomedicine, knowing how to interpret the results obtained and arrive at well-founded conclusions C3. Be able to transmit knowledge both orally and in writing, to a specialised and non-specialised audience, working in multidisciplinary and international teams. C4. To develop, organize and plan their work by making the right decisions based on available information, gathering and interpreting relevant data to make judgments within their area of study.

1.- Introduction to fluid mechanics 1.1. Solids, liquids and gases 1.2. The continuum hypothesis 1.3. Density, velocity and internal energy 1.4. Local thermodynamic equilibrium. Equations of state. 2.- Kinematics of the fluid flow 2.1. Eulerian and Lagrangian descriptions 2.2. Uniform flow. Steady flow. Stagnation points. 2.3. Trajectories. Paths. Streamlines. 2.4. Substantial derivative. Acceleration. 2.5. Circulation and vorticity. Irrotational flow. Velocity potential. 2.6. Stream function 2.7. Strain-rate tensor 2.8. Convective flux. Reynolds transport theorem. 3.- Conservation laws in fluid mechanics 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. Angular momentum equation. 3.6. Heat conduction vector. Energy equation in integral form. 4.- The Navier-Stokes equations 4.1. Navier-Stokes equations. 4.2. Initial and boundary conditions. 4.3. Bernoulli¿s equation 5.- Dimensional analysis 5.1. Dimensional analysis. The Pi theorem. 5.2. Applications 5.3. Nondimensionalization of the Navier-Stokes equations 5.4. Dimensionless numbers in fluid mechanics 6.- Viscous flows with applications to biomedical problems: circulatory flow, flow in airways, flow at the cell's scale 6.1. Unidirectional flows 6.2. The Stoke's problem 6.3. Quasi-one-directional flow 6.4. Applications to flows of interest in biology

Lectures: the main concepts of fluid mechanics are derived rigorously using physical and mathematical tools. Seminars: the concepts derived in the lectures are used to solve problems. Also, new concepts are introduced through examples. Homework: homeworks covering different areas of Fluid Mechanics are given to the students. Lab sessions: the students will become familiar with the usage of numerical (computational) and experimental tools to investigate a canonical flow of biomedical interest.