# ADVANCED FLUID MECHANICS

OVERVIEW

The course introduces the student to the study of fluid mechanics showing the equations

that control the motion of a fluid and obtaining some particular solutions of the hydrodynamic problem in order to provide the essential skills that are necessary to face practical problems

## AIMS AND CONTENT

AIMS AND LEARNING OUTCOMES

the frequency and the active participation in the training activities (lectures and exercises) will allow the student 1) to formulate the problem of fluid motion in the correct way, 2) to identify the most appropriate approach to obtain the solution, according to the values

of the parameters that control the flow of fluids, 3) to evaluate the forces that the fluids exert on moving bodies or, in a similar way, to determine the forces exerted by a fluid that flows around a structure. At the end of the course, the student will be able to describe the motion of a fluid both in the laminar regime (for example the motion inside the circulatory system) and in the turbulent regime (for example the motion along a river or the motion generated by the wind that flows around a building) and to evaluate the forces exerted

from a wave against a breakwater or to estimate the lift that keeps an airplane in flight.

PREREQUISITES

To follow the course successfully, it is necessary to know the basic principles of physics and thermodynamics, which however will be briefly recalled during the course. Furthermore, the knowledge provided by the courses of analysis and mathematical physics is essential

Teaching methods

The course consists of lectures for a total of about 50 hours

and exercises for a total of about 10 hours. The attendance at lessons and exercises is strongly recommended.

SYLLABUS/CONTENT

Continuum approach.

Properties of fluids.

Kinematics of fluids.

Stress tensor.

Cardinal equations of fluid motion.

Elements of thermodynamics.

Boundary conditions.

Constitutive laws.

Navier-Stokes equations.

Laminar flows.

Vorticity dynamics.

Flows at high Reynolds numbers.

Dynamics of inviscid fluids: Bernoulli's theorem.

Irrotational flows.

Conformal transformations.

Boundary layer: basic equations and physical interpretations.

Blasius boundary layer.

Turbulence: equations of the mean motion.

The problem of the closure of turbulent flows and Boussinesq approach.

Outline of the main turbulence models.

RECOMMENDED READING/BIBLIOGRAPHY

- Blondeaux P. and Vittori G. (2018)

Dispense dei corsi di Idrodinamica e Meccanica dei Fluidi

Book available in electronic format

Further books

- Marchi E. and Rubatta A. (1981)

Meccanica dei fluidi. Principi e applicazioni

UTET, ISBN: 8802036594

- Ghetti A. (1980)

Idraulica

Libreria Cortina, Padua, ISBN: 8877840528

- Batchelor G.K. (2000)

An introduction to fluid dynamics

Cambridge University Press, ISBN: 9780511800955

## TEACHERS AND EXAM BOARD

Exam Board

ALESSANDRO STOCCHINO (President)

PAOLO BLONDEAUX (President)

GIOVANNA VITTORI

GIOVANNI BESIO

## LESSONS

Teaching methods

The course consists of lectures for a total of about 50 hours

and exercises for a total of about 10 hours. The attendance at lessons and exercises is strongly recommended.

LESSONS START

17 september 2018

## EXAMS

Exam description

The exam consists of an oral examination during which the student will have to show that she/he has learned the topics explained during the course and the capability to formulate correctly a hydrodynamic problem as well as to choose the most appropriate approach to determine the relative solution

Assessment methods

The exam aims at ascertaining the following aspects of student's preparation:

1) knowledge acquired about the basic concepts of the course, 2) capability to apply the knowledge acquired within specific contexts. The possession of these components

of the student's preparation will be ascertained through specific questions.