Calculus I and II Linear algebra Differential equations 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.

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.- Flow in ducts with biomedical applications: circulatory flow, flow in airways 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: two homework 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.