Fluid Mechanics

Continuum hypothesis. Viscosity concept. Hydro- and aerostatics, pressure forces on surfaces. Buoyancy. Stability. Accelerating systems. Principles of fluid motion, velocity field, streamlines. Transport theorem. Laminar and turbulent motion. Control volumes. Equation of continuity. Energy equation and Bernoulli's equation. Momentum equation. Differential methods, vorticity and circulation. Stream function. Euler's equation. Navier-Stokes' equation. Viscous stress tensor. Drag and lift, Kutta-Joukowsky's theorem. The Magnus effect. Potential flow, superposition of singularities. Water waves. Complex potentials.

Knowledge:
After completion of this course, the student should have knowledge about:
- Fluid properties, viscosity.
- Velocity field, substantial derivative, streamlines and pathlines.
- Pressure distribution in stationary and accelerated systems. Rotating container. Buoyancy.
- Reynolds’ transport theorem.
- Continuity equation, momentum equation and angular momentum equation for control volumes.
- Energy equation and Bernoulli equation.
- Euler equations for inviscid flow.
- Navier-Stokes equations for viscous flow.
- Boundary conditions for the basic equations of fluid mechanics.
- Drag and lift.
- Stream function, vorticity and rotation, viscous stresses.
- Reynolds’ number. Qualitative issues on turbulence.
- The Kutta-Joukowsky theorem.
- The Magnus effect.
- Two-dimensional potential theory, velocity potential, some elementary flows.
- Water waves.
- Complex potentials.

Skills:
After completion of this course, the student will have skills on:
- Evaluation of models for flow analysis.
- Use of control volume analysis.
- Computation of forces and moments from fluid on solid bodies.
- Solution of the basic laws of fluid mechanics for simple flow problems.
- Basic theory for surface waves.
- How to make use of complex potential theory.

General competence:
After completion of this course, the student will have general competence on:
- The basic elements of the theoretical foundations for ideal and real fluid flows.
- Formulation and solution of practical flow problems.

Lectures and exercises. At least 2/3 of the exercises must be approved before final exam.