Advanced Topics in Fluid Mechanics


Know how to express and how to interpret results expressed by dimensionless parameters as, not being restricted to the area of ​​fluid mechanics. To understand the problem of similarity in the modeling of situations of practical interest.

Learn and apply knowledge to deal with the effects of roughness and boundary layer separations. Have knowledge of theoretical tools and their application to different flow regimes (laminar, turbulent) or regions of the flows. In this sense, know turbulence fundamentals and: determine and use integral limit-layer parameters; to achieve dexterity in the manipulation of the differential equations that govern the flows to reach results that allow to analyze them; to know the effects of the longitudinal pressure gradient in the development of boundary layers; know how to use pressure coefficients for bodies immersed in flows, comprising and respecting ranges of applicability.

To learn and know how to apply the fundamentals of flow studies where the effects of compressibility can not be overlooked. To know the phenomenon of choking, the operation of converging-divergent nozzles, and shock waves, and know how to perform calculations in this scope, also with the use of tabulated information. Know how to solve problems of fluid mechanics in the aforementioned areas, within the broad scope of Engineering and, in particular, mechanical engineering.

To develop capacities of: information processing, autonomous work and self-learning, problem solving at the engineering level, application of knowledge to new situations.

General characterization





Responsible teacher

Diana Filipa da Conceição Vieira, José Fernando de Almeida Dias, Moisés Gonçalves de Brito


Weekly - 4

Total - 64

Teaching language



The programme assumes that the student masters the matters studied in «Dinâmica dos Fluidos I» (code 3658).


White, F. M., “Fluid Mechanics”, McGraw-Hill.

Oliveira, L. A. e Lopes, A. G., “Mecânica dos Fluidos”, LIDEL.

Tennekes, H. and Lumley, J. L., "A First Course in Turbulence", MIT Press.

Teaching method

The study-matter is presented in the theoretical-exercise-solving classes, followed immediately by the statement and discussion, by the professor, of problems of practical application, which are then solved by the students. At a certain point of the semester, the students carry out a laboratory work, in group.

Evaluation method

1 - Assessment mode

1.1 Continuous assessment, through 2 elements: two written tests (theoretical-practical component).

1.2 There is «Frequência» - through a laboratory work.

2 - Final grade

2.1. The final grade is calculated as

Final grade = 0.45 x (test 1) + 0.4 x (test 2) + 0.15 x (laboratory work)


Final grade = 0.85 x (final exam) + 0.15 x (laboratory work).

2.2. The values enter in the calculation rounded to the first decimal place. For approval, the final grade has to be greater or equal to 9.5 val.

2.3. If a students''s final grade (already rounded to the nearest integer) is equal or greater than 17 val., an oral exam may be scheduled for "grade defense".

3 - Rules for the written examinations

Only answers written in ink shall be admitted; the use of text-memory calculators is not allowed; the use of mobile phones is forbidden (not even as watch or calculator). Transgressions shall be dealt as by  RAC.

Subject matter

Dimensional analysis and physical similitude. Application of Buckingham''s Π theorem to cases studied in th CU. Similitude, modelling and pitfalls.

Differential equations. Differential equations of mass and momentum conservation. The Navier-Stokes equations for Newtonian flows and Euler equations for inviscid flows. Dimensionless forms of these equations.

 Turbulence. Universal characteristics of turbulence. Reynolds decompostion. Modeling turbulent flow.

– Boundary layer flows. Prandtl''s theory; brief reference to inviscid flow. Boundary layer over a flat plate. Von Kármán''s integral analysis. Blasius'' exact solution. Structure of the turbulent boundary layer. Boundary layer with longitudinal pressure gradient. Thwaites'' method of determining the separation point. Bodies immersed in flows: friction and pressure components of the resulting force; experimental drag and lift coefficients.

Compressible flows. The speed of sound; Mach number. Perfect gases (revision). Isentropic and adiabatic flow. Isentropic flow with changes in cross-sectional area. The normal shock wave. The converging-diverging duct. Prandtl-Meyer expansion waves.


Programs where the course is taught: