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Fluids and Superfluids

Code: 100179
Credits: 6
2026/2027
Degree programme Type Course
Physics OP 4

Contact lecturer

Name :
Francisco Javier Bafaluy Bafaluy
Email :
javier.bafaluy@uab.cat

Teaching staff

Albert Beardo Ricol

Group languages

You can consult this information at the end of the document.

Prerequisites

There are no official requirements. Knowledge of Newtonian Physics and Thermodynamics, ordinary and partial differential equations is assumed; also basic knowledge of quantum mechanics.

Objectives

  • Introduce the concepts and methods of the physics of continuous media.
  • Understand the basic dynamical properties of liquids.
  • Understand and describe the dynamic regimes of Newtonian liquids.
  • Apply the fundamental concepts in the previous items to different applications and situations of interest.
  • Phenomenologically describe the behavior of superfluid helium.
  • Use statistical procedures to describe turbulent flows.

Learning outcomes

  1.  Carry out academic work independently using bibliography (especially in English), databases and through collaboration with other professionals
  2. Communicate complex information in an effective, clear and concise manner, either orally, in writing or through ICTs, in front of both specialist and general publics.
  3. Use critical reasoning, show analytical skills, correctly use technical language and develop logical arguments
  4. Work independently, take initiative itself, be able to organize to achieve results and to plan and execute a project.
  5. Working in groups, assume shared responsibilities and interact professionally and constructively with others, showing absolute respect for their rights.
  6. Determine the velocity field of perfect fluids through Euler's equation.
  7. Determine the velocity field of dissipative fluids through Navier-Stokes' equation.
  8. Determine the field of pressures and the forces exerted on walls containing a fluid.
  9. Phenomenologically describe the behaviour of superfluid helium on the model of Tisza.
  10. Describe the general aspects of hydrodynamic turbulence.
  11. Reduce Navier-Stokes' equation in the boundary Establisher of an analytically solvable expression.
  12. Justify Oseen's equation for the movement of a sphere within a fluid of low Reynolds number.
  13. Use the methods of solving partials differential equations to solve the equations of fluid and solid movement in fluids.
  14. Use statistical procedures to describe turbulent flow.
  15. Carry out a project that relates the concepts of fluid dynamics with current innovative issues and present the results.
  16. Identify situations in which a change or improvement is needed.
  17. Identify the social, economic and environmental implications of academic and professional activities within one's own area of knowledge.

Contents

  1. Physics of continuous media
  2. Fluid kinematics
  3. Perfect fluids
  4. Newtonian fluids
  5. Dynamic similarity
  6. Flow at large and small Reynolds numbers
  7. Boundary layers
  8. Superfluids: liquid helium
  9. Hydrodynamic instabilities
  10. Turbulence

Learning activities and methodology

Title Hours ECTS Learning outcomes
Exercise solving 47 1.88 1, 2, 3, 4, 5
Theory classes 33 1.32 2, 3, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15
Practical classes 16 0.64 3, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15
Personal or group study 45 1.8 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15

- Theory classes: The concepts and methods of the different subjects will be introduced, with a variety of examples.


- Problems classes: Teachers will solve selected exercises from a collection that will be available to the students beforehand.


- Autonomous work: It is imperative that students complement face-to-face activities with autonomous, individual or group work; to practice the resolution of problems is especially important.

Annotation: within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.

Assessment

Continuous assessment activities

Title Weight Hours ECTS Learning outcomes
Recovery exam 80% 3 0.12 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16
First term test 40 % 3 0.12 2, 3, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15
Exercices delivery 20 % 0 0 1, 2, 3, 4, 5, 17
Second term test 40 % 3 0.12 2, 3, 4, 7, 8, 9, 10, 11, 12, 13, 14

- Two partial tests including theory and problems (80% of the final grade, each 40%); delivery of selected exercises (20% of the final grade).

- In case of not reaching the minimum grade to pass, a recovery exam with all the topics of the course may be carried out. The grade of this exam will replace the grade corresponding to the partial exams.

- In order to be able to take the recovery exam it will be necessary to have submitted to the two partial exams.


Single Assessment:

Students who follow the single evaluation modality must:

- Deliver the same exercises the other students do, with the same deadline if possible or, if this is not possible the same day of the single assessment (20%).

- Take a final test that will correspond to the two partial tests (80%). This exam will take place at the same day, hour and location as the second partial test of the continuous evaluation.

- If necessary, students could take the same recovery exam as the rest of the students.

Use of AI:

In this course, the use of Artificial Intelligence (AI) technologies is permitted exclusively for bibliographic or information searches. For graded assignments, it is essential to clearly identify which parts were generated using this technology, specify the tools used, and include a critical reflection on how these tools influenced the process and the final result of the activity. Lack of transparency regarding the use of AI in these activities will be considered a breach of academic integrity and could result in a partial or full penalty on the assignment grade, or more severe sanctions in cases of serious misconduct.

Bibliography

  • Kundu, Pijush K. (2024). Fluid mechanics (7th ed.) Elsevier Available in the library and online (5a ed. 2014)
  • Landau, L. D. & Lifshits̅, E. M. (1987). Fluid mechanics (2nd ed.) Pergamon Press Available online and in the library
  • Lautrup, Benny. (2011). Physics of continuous matter : exotic and everyday phenomena in the macroscopic world (2nd ed.) Taylor & Francis Available online
  • Tritton, D.J. (1988). Physical Fluid Dynamics, (2nd ed.) Oxford University Press; Clarendon Press Available in the library

Software

No específic software is required.

Course groups and languages

The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE

Type of teaching Group Language Semester Shift
(TE) Theory 1 Catalan first semester morning-mixed
(PAUL) Classroom practices 1 Catalan first semester morning-mixed