Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Academic calendar
The academic calendar shows the deadlines and scheduled events that are relevant to students, teaching and technical-administrative staff of the University. Public holidays and University closures are also indicated. The academic year normally begins on 1 October each year and ends on 30 September of the following year.
Course calendar
The Academic Calendar sets out the degree programme lecture and exam timetables, as well as the relevant university closure dates..
Period | From | To |
---|---|---|
Primo semestre | Oct 4, 2021 | Jan 28, 2022 |
Secondo semestre | Mar 7, 2022 | Jun 10, 2022 |
Session | From | To |
---|---|---|
Sessione invernale d'esame | Jan 31, 2022 | Mar 4, 2022 |
Sessione estiva d'esame | Jun 13, 2022 | Jul 29, 2022 |
Sessione autunnale d'esame | Sep 1, 2022 | Sep 30, 2022 |
Session | From | To |
---|---|---|
Sessione estiva di laurea | Jul 21, 2022 | Jul 21, 2022 |
Sessione autunnale di laurea | Oct 13, 2022 | Oct 13, 2022 |
Sessione autunnale di laurea - dicembre | Dec 7, 2022 | Dec 7, 2022 |
Sessione invernale | Mar 16, 2023 | Mar 16, 2023 |
Period | From | To |
---|---|---|
Festa di Tutti i Santi | Nov 1, 2021 | Nov 1, 2021 |
Festa dell'Immacolata Concezione | Dec 8, 2021 | Dec 8, 2021 |
Festività natalizie | Dec 24, 2021 | Jan 2, 2022 |
VACANZE DI PASQUA | Apr 15, 2022 | Apr 19, 2022 |
FESTA DEL LAVORO | May 1, 2022 | May 1, 2022 |
Festa di San Zeno - S. Patrono di Verona | May 21, 2022 | May 21, 2022 |
Festa della Repubblica | Jun 2, 2022 | Jun 2, 2022 |
Chiusura estiva | Aug 15, 2022 | Aug 20, 2022 |
Exam calendar
Exam dates and rounds are managed by the relevant Science and Engineering Teaching and Student Services Unit.
To view all the exam sessions available, please use the Exam dashboard on ESSE3.
If you forgot your login details or have problems logging in, please contact the relevant IT HelpDesk, or check the login details recovery web page.
Should you have any doubts or questions, please check the Enrollment FAQs
Academic staff
Study Plan
The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.
1° Year
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2° Year activated in the A.Y. 2022/2023
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3° Year activated in the A.Y. 2023/2024
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Legend | Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Fluid dynamics (2023/2024)
Teaching code
4S00258
Teacher
Coordinator
Credits
6
Also offered in courses:
- Fluid dynamics of the course Bachelor's degree in Human Centered Medical System Engineering
Language
Italian
Scientific Disciplinary Sector (SSD)
ING-IND/06 - FLUID DYNAMICS
Period
Semester 2 dal Mar 4, 2024 al Jun 14, 2024.
Courses Single
Authorized
Learning objectives
Derivation of the fluid-dynamic equations from conservation laws in Physics; discussion on the rheological structure of fluids and the model for Newtonian fluids; different flows and simplifications of the governing equations; Bernoulli theorem in all forms and for all cases; some exact solutions; vorticity dynamics; laminar boundary layer; stability and transition; turbulence; hyperbolic equations in fluid dynamics. Numerical resolution in Matlab / Octave of some typical problems of fluid dynamics.
Prerequisites and basic notions
Differential calculus in several variables, ordinary and partial differential equations, main numerical methods for differential equations, knowledge of at least one scientific computing environment.
Program
The teaching prerequisites are: differential and integral calculus in one and two variables, numerical methods for the solution of equations and systems of nonlinear equations, basic numerical methods for differential equations, such as explicit Euler and the finite difference method.
1. Introduction to fluids: definitions, continuous hypothesis and properties of fluids; differences between fluid, flux, flow; some kinematics (stream-lines, trajectories, streak-lines), forces and stresses (Cauchy Theorem and symmetry of the stress tensor), the constitutive relation for Newtonian fluids (viscous stress tensor).
2. Governing equations: Eulerian vs Lagrangian approach; control volume and material volume, conservation of mass in a fixed volume, time derivative of the integral over a variable domain, Reynolds Theorem (scalar and vectorial forms), conservation of mass in a material volume, from conservation laws to the Navier-Stokes equations, the complete Navier-Stokes equations (in conservative, tensorial form), substantial derivative, conservative vs convective form of the equations, alternative forms of the energy equation, dimensionless equations, initial and boundary conditions.
3. Particular cases of the governing equations: time dependence, effect of viscosity, thermal conduction, entropy, compressibility, barotropic flows, incompressible flows, ideal flows, Euler equations irrotational flows, barotropic and non-viscous flows: Crocco's form, Bernoulli theorem in all cases and forms.
4. Some exact solutions: incompressible and parallel flows, infinite channel flow, Couette and Poiseuille flows, flow in a circular pipe, Hagen-Poiseuille solution.
5. Vorticity dynamics: preliminary definitions, vorticity equation in the general case, special cases (constant density, non-viscous flow with conservative external field), Kelvin's theorem, Helmholtz's theorems and their geometrical meaning.
6. Laminar boundary layer: Prandtl theory, boundary layer past a flat plate, derivation of Blasius' equation (similar solutions), boundary-layer thickness, drag due to skin-friction, characteristics of a boundary layer (displacement thickness, momentum thickness, shape factor), integral von Kàrmàn equation, numerical solution of the 2D steady equations for the boundary layer past a flat plate:
(a) parabolic PDE + BC (Prandtl's equations): marching in space
(b) ODE + BC (Blasius' equation): nonlinear boundary value problem
(c) comparison between the two methods.
7. Stability and transition: flow in a pipe - Reynolds' experiment, transition in a laminar boundary layer, linear stability for parallel flows (Orr-Sommerfeld equation),
Squire's theorem, non-viscous stability (Rayleigh's criteria), viscous stability, linear stability curves.
8. Turbulence: phenomenological characteristics, turbulent scales, energy cascade, Kolmogorov's theory, DNS (Direct numerical simulation), RANS (Reynolds-Averaged-Navier-Stokes equations), the problem of closure for the RANS, closure models, Boussinesq hypothesis for the tutbulent viscosity (models of order 0, 1 and 2), LES (Large Eddy Simulation).
9. Hyperbolic differential equations in fluid dynamics: main characteristics and comparison with parabolic and elliptic equations, conservation laws, transport equation, characteristic lines, Riemann problem, Burgers' equation, weak solutions, shock waves, rarefaction waves, comparison between conservative and non-conservative numerical methods, method of characteristics, usage of an applet for the visualization of shock and rarefaction waves, hyperbolic linear and non-linear systems, genuine nonlinearity, linear degeneration, contact discontinuity, solution of the Riemann for the Euler equations.
Bibliography
Didactic methods
The course takes place through lectures on the blackboard. During the course some fluid dynamics problems will be proposed to be solved numerically on the computer.
Learning assessment procedures
Oral exam lasting about 45 minutes on all the topics covered and including questions on the codes developed by the student.
Evaluation criteria
The aim of the exam is to ensure that the student is able to produce and recognize rigorous demonstrations, mathematically formalize natural language problems and discuss mathematical models for fluid dynamics analyzing their limits and applicability. The exam consists of an oral interview on the course program and the discussion on the numerical exercises in Matlab/Octave assigned during the course. The discussion on the latter aims to ensure that the student is able to use computer tools, programming languages, and specific software.
Criteria for the composition of the final grade
The final mark is calculated on the basis of the answers given during the oral interview to the individual questions on the course program and on the numerical resolution of the problems assigned during the class
Exam language
Italiano o inglese su richiesta / Italian or English on demand
Type D and Type F activities
Le attività formative di tipologia D sono a scelta dello studente, quelle di tipologia F sono ulteriori conoscenze utili all’inserimento nel mondo del lavoro (tirocini, competenze trasversali, project works, ecc.). In base al Regolamento Didattico del Corso, alcune attività possono essere scelte e inserite autonomamente a libretto, altre devono essere approvate da apposita commissione per verificarne la coerenza con il piano di studio. Le attività formative di tipologia D o F possono essere ricoperte dalle seguenti attività.
1. Insegnamenti impartiti presso l'Università di Verona
Comprendono gli insegnamenti sotto riportati e/o nel Catalogo degli insegnamenti (che può essere filtrato anche per lingua di erogazione tramite la Ricerca avanzata).
Modalità di inserimento a libretto: se l'insegnamento è compreso tra quelli sottoelencati, lo studente può inserirlo autonomamente durante il periodo in cui il piano di studi è aperto; in caso contrario, lo studente deve fare richiesta alla Segreteria, inviando a carriere.scienze@ateneo.univr.it il modulo nel periodo indicato.
2. Attestato o equipollenza linguistica CLA
Oltre a quelle richieste dal piano di studi, per gli immatricolati dall'A.A. 2021/2022 vengono riconosciute:
- Lingua inglese: vengono riconosciuti 3 CFU per ogni livello di competenza superiore a quello richiesto dal corso di studio (se non già riconosciuto nel ciclo di studi precedente).
- Altre lingue e italiano per stranieri: vengono riconosciuti 3 CFU per ogni livello di competenza a partire da A2 (se non già riconosciuto nel ciclo di studi precedente).
Tali cfu saranno riconosciuti, fino ad un massimo di 6 cfu complessivi, di tipologia F se il piano didattico lo consente, oppure di tipologia D. Ulteriori crediti a scelta per conoscenze linguistiche potranno essere riconosciuti solo se coerenti con il progetto formativo dello studente e se adeguatamente motivati.
Gli immatricolati fino all'A.A. 2020/2021 devono consultare le informazioni che si trovano qui.
Modalità di inserimento a libretto: richiedere l’attestato o l'equipollenza al CLA e inviarlo alla Segreteria Studenti - Carriere per l’inserimento dell’esame in carriera, tramite mail: carriere.scienze@ateneo.univr.it
3. Competenze trasversali
Scopri i percorsi formativi promossi dal TALC - Teaching and learning center dell'Ateneo, destinati agli studenti regolarmente iscritti all'anno accademico di erogazione del corso https://talc.univr.it/it/competenze-trasversali
Modalità di inserimento a libretto: non è previsto l'inserimento dell'insegnamento nel piano di studi. Solo in seguito all'ottenimento dell'Open Badge verranno automaticamente convalidati i CFU a libretto. La registrazione dei CFU in carriera non è istantanea, ma ci saranno da attendere dei tempi tecnici.
4. Periodo di stage/tirocinio
Oltre ai CFU previsti dal piano di studi (verificare attentamente quanto indicato sul Regolamento Didattico): qui informazioni su come attivare lo stage.
Insegnamenti e altre attività che si possono inserire autonomamente a libretto
Documents and news
- Modifiche al piano di studi (.doc) (octet-stream, it, 1314 KB, 30/06/21)
years | Modules | TAF | Teacher |
---|---|---|---|
1° 2° 3° | Algorithms | D |
Roberto Segala
(Coordinator)
|
1° 2° 3° | Basis of general chemistry | D |
Chiara Nardon
|
1° 2° 3° | Genetics | D |
Massimo Delledonne
(Coordinator)
|
years | Modules | TAF | Teacher |
---|---|---|---|
1° 2° 3° | Algorithms | D |
Roberto Segala
(Coordinator)
|
1° 2° 3° | LaTeX Language | D |
Enrico Gregorio
(Coordinator)
|
1° 2° 3° | Organization Studies | D |
Serena Cubico
(Coordinator)
|
1° 2° 3° | History and Didactics of Geology | D |
Guido Gonzato
(Coordinator)
|
years | Modules | TAF | Teacher | |
---|---|---|---|---|
1° | Subject requirements: mathematics | D |
Franco Zivcovich
|
|
1° 2° 3° | ECMI modelling week | F | Not yet assigned | |
1° 2° 3° | ESA Summer of code in space (SOCIS) | F | Not yet assigned | |
1° 2° 3° | Google summer of code (GSOC) | F | Not yet assigned | |
1° 2° 3° | Python programming language | D |
Giulio Mazzi
(Coordinator)
|
Career prospects
Module/Programme news
News for students
There you will find information, resources and services useful during your time at the University (Student’s exam record, your study plan on ESSE3, Distance Learning courses, university email account, office forms, administrative procedures, etc.). You can log into MyUnivr with your GIA login details: only in this way will you be able to receive notification of all the notices from your teachers and your secretariat via email and soon also via the Univr app.
Graduation
Documents
Title | Info File |
---|---|
1. Come scrivere una tesi | pdf, it, 31 KB, 29/07/21 |
2. How to write a thesis | pdf, it, 31 KB, 29/07/21 |
5. Regolamento tesi | pdf, it, 171 KB, 20/03/24 |
List of theses and work experience proposals
theses proposals | Research area |
---|---|
Formule di rappresentazione per gradienti generalizzati | Mathematics - Analysis |
Formule di rappresentazione per gradienti generalizzati | Mathematics - Mathematics |
Proposte Tesi A. Gnoatto | Various topics |
Mathematics Bachelor and Master thesis titles | Various topics |
THESIS_1: Sensors and Actuators for Applications in Micro-Robotics and Robotic Surgery | Various topics |
THESIS_2: Force Feedback and Haptics in the Da Vinci Robot: study, analysis, and future perspectives | Various topics |
THESIS_3: Cable-Driven Systems in the Da Vinci Robotic Tools: study, analysis and optimization | Various topics |
Stage | Research area |
---|---|
Internship proposals for students in mathematics | Various topics |
Attendance
As stated in the Teaching Regulations for the A.Y. 2022/2023, except for specific practical or lab activities, attendance is not mandatory. Regarding these activities, please see the web page of each module for information on the number of hours that must be attended on-site.
Career management
Student login and resources
Erasmus+ and other experiences abroad
Commissione tutor
La commissione ha il compito di guidare le studentesse e gli studenti durante l'intero percorso di studi, di orientarli nella scelta dei percorsi formativi, di renderli attivamente partecipi del processo formativo e di contribuire al superamento di eventuali difficoltà individuali.
E' composta dai proff. Sisto Baldo, Marco Caliari, Francesca Mantese, Giandomenico Orlandi e Nicola Sansonetto