Subject Datasheet
Download PDFI. Subject Specification
1. Basic Data
1.1 Title
Theoretical hydrodynamics
1.2 Code
BMEEOVVDT71
1.3 Type
Module with associated contact hours
1.4 Contact hours
| Type | Hours/week / (days) |
| Lecture | 2 |
1.5 Evaluation
Exam
1.6 Credits
3
1.7 Coordinator
| name | Dr. János Józsa |
| academic rank | Professor |
| jozsa.janos@bme.hu |
1.8 Department
Department of Hydraulic and Water Resources Engineering
1.9 Website
1.10 Language of instruction
hungarian and english
1.11 Curriculum requirements
Ph.D.
1.12 Prerequisites
Recommended courses: Any courses on hydrodynamics and partial differential equations and vector fields.
1.13 Effective date
1 September 2022
2. Objectives and learning outcomes
2.1 Objectives
The aim of the subject is to familiarize the student with the mathematical foundations and basic equations of fluid dynamics.
2.2 Learning outcomes
Upon successful completion of this subject, the student:
A. Knowledge
- Knowledge of the basic concepts of partial differential equations and vector fields.
- Knowledge of the basic kinematic and dynamic concepts necessary to describe the liquid as a continuum.
- Knowledge of the basic equation of fluid dynamics and its most important features.
- Knowledge of the vorticity transport equation derived from the basic equation of fluid dynamics. Knowledge of the general geometric formulation of two- and three-dimensional hydrodynamics.
B. Skills
- Advanced problem-solving capacity in mathematics and physics, especially on algebraic manipulations.
- Ability to formulate a hydrodynamic model, such as the complex of physical environment, mathematical equations and boundary conditions.
C. Attitudes
- Cooperates with the instructor during the learning process.
- Continuously and actively seeks ways of gaining knew knowledge even beyond the required curriculum and employs the internet for finding intuitive answers to research problems.
D. Autonomy and Responsibility
- Participates in lectures and prepares for the exam.
2.3 Methods
Lectures on theory.
2.4 Course outline
| Week | Topics of lectures and/or exercise classes |
| 1. | Introduction: partial differential equations and vector fields. |
| 2. | Introduction: partial differential equations and vector fields. |
| 3. | Introduction: partial differential equations and vector fields. |
| 4. | The continuum model of the fluid. Velocity, acceleration. The acceleration as a Lie-derivative. |
| 5. | Description of streamlines. The velocity field as a transformation on streamlines. Continuous transformation groups. |
| 6. | Conservation of the matter. Divergence of the velocity field. |
| 7. | Rotation of a fluid element. Vorticity of the velocity field. |
| 8. | Incompressible and irrotational plane flows. Laplace equation. |
| 9. | The vorticity of the acceleration. Lie-bracket of vector fields. Commuting flows. |
| 10. | Circulation. Vortex theorems. |
| 11. | The Cauchy stress tensor. Navier-Stokes equations. |
| 12. | Navier-Stokes, Euler, and Bernoulli equations. |
| 13. | The vorticity transport equations. Geometric picture of fluid flows. |
| 14. | Dimensionless numbers. The dimensionless form of Navier-Stokes equations. The appearance of viscosity, as a symmetry breaking. |
The above programme is tentative and subject to changes due to calendar variations and other reasons specific to the actual semester. Consult the effective detailed course schedule of the course on the subject website.
2.5 Study materials
a) Textbooks:
- Andreev, V.K., et al., 1998. Application of Group-Theoretical Methods in Hydrodynamics, Kluwer.
- Arnold, V.I., 1974. Mathemtical Methods of Classical Mechanics, Springer.
- Batchelor, G.K., 1967. An Introduction to Fluid Dynamics, Cambridge University Press.
- Olver, P. J., 1986. Application of Lie Groups to Differential Equations, Springer.
2.6 Other information
None
2.7 Consultation
Time of consultations: previously agreed times.
This Subject Datasheet is valid for:
Inactive courses
II. Subject requirements
Assessment and evaluation of the learning outcomes
3.1 General rules
Evaluation of the participant’s learning progress described in 2.2. is performed by an oral exam.
3.2 Assessment methods
| Evaluation form | Abbreviation | Assessed learning outcomes |
| Oral exam | V | A.1-A.4; B.1-B.2; C.1-C.2; D.1 |
The dates of deadlines of assignments/homework can be found in the detailed course schedule on the subject’s website.
3.3 Evaluation system
| Abbreviation | Score |
| V | 100% |
| Sum | 100% |
3.4 Requirements and validity of signature
At least 70% of the attendance of the classes is expected.
3.5 Grading system
If the grade for the exam is at least satisfactory, the final grade is the grade for the exam.
3.6 Retake and repeat
3.7 Estimated workload
| Activity | Hours/semester |
| participation in contact classes | 14×2=28 |
| study from notes, textbooks, preparation for the exam | 62 |
| Sum | 90 |
3.8 Effective date
1 September 2022
This Subject Datasheet is valid for:
Inactive courses