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1. Course title

Dimension analysis


2. Course code

ATM365


3. Course status: compulsory or optional

-Which degree programme is responsible for the course?
Master's Programme in Atmospheric Sciences

-Which module does the course belong to?
ATM3003 Advanced Studies in Geophysics of the Hydrosphere

-Is the course available to students from other degree programmes?
Yes


4. Course level (first-, second-, third-cycle/EQF levels 6, 7 and 8)


-Master’s level, degree programmes in medicine, dentistry and veterinary medicine = secondcycle
degree/EQF level 7
-Doctoral level = third-cycle (doctoral) degree/EQF level 8
-Does the course belong to basic, intermediate or advanced studies (cf. Government Decree
on University Degrees)?,

advanced


5. Recommended time/stage of studies for completion


This course focuses on the main concepts and methods of dimensional analysis and their application to physical problems. The course target group are students of hydrospheric geophysics but students from other study tracks are welcome as well. The principles of dimensional analysis has proved useful in geosciences - meteorology, oceanography and hydrology.


6. Term/teaching period when the course will be offered



7. Scope of the course in credits

5 cr

8. Teacher coordinating the course

Ekaterina Ezhova

9. Course learning outcomes


Upon completing of the course, the student will

- learn about the main concepts and methods of dimensional analysis - basic dimensions, dimensionless groups, Rayleigh algorithm, Buckingham Pi-theorem;

- apply the methods of dimensional analysis to relevant problems of mechanics, fluid dynamics and thermodynamics;

- assess the application of dimensional analysis in meteorology, hydrology and oceanography.


10. Course completion methods

The course consists of lectures and seminars where students solve problems. 

11. Prerequisites


Basic knowledge of linear algebra (rank of matrix) is useful, but there will be separate lectures devoted to relevant mathematical methods.


12. Recommended optional studies




13. Course content


Dimensional analysis examines relationships between physical quantities such as velocity, time, force etc. Each quantity can be expressed in powers of a selected set of basic quantities or dimensions. By dimensional analysis methods, relationships between quantities can be established requiring that the relationships are dimensionally consistent. E.g., it can be shown that drag force in fluid flow depends on the Reynolds number and squared flow speed. This course presents the ideas of dimensional analysis, Buckingham Pi-theorem, applications of dimensional analysis to mechanics, fluid dynamics and thermodynamics. Furthermore, scaling issues and similarity models are discussed based on dimensional analysis. During the course, we will discuss applications of dimensional analysis within different geophysical sciences such as hydrology, oceanography and meteorology.


14. Recommended and required literature


Required literature:

  • Lemons D. (2017) A Student’s Guide to Dimensional Analysis. Cambridge University Press.

Recommended literature:

  • Andrew C. Palmer (2008) Dimensional analysis and intelligent esperimentation. World Scientific.


15. Activities and teaching methods in support of learning


Lectures and seminars. 


16. Assessment practices and criteria, grading scale


Final exam. Grading 1-5.

17. Teaching Language

English

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