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Biomechanics of Continuum Media II (Fluids)
Engineering & Social Sciences Program
Madrid, Spain
Dates: mid Jan 2026 - early Jun 2026
Biomechanics of Continuum Media II (Fluids)
OVERVIEW
CEA CAPA Partner Institution: Universidad Carlos III de Madrid
Location: Madrid, Spain
Primary Subject Area: Biomedical Engineering
Instruction in: English
Course Code: 15544
Transcript Source: Partner Institution
Course Details: Level 200
Recommended Semester Credits: 3
Contact Hours: 42
Prerequisites: Calculus I and II, Linear algebra, Differential equations, Biomechanics of continuum media I (solid mechanics)
DESCRIPTION
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
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