Advanced Topics in Fluid Mechanics


Knowing how to interpret results expressed by dimensionless parameters as well as knowing how to express results in this way, not being restricted to the area of ​​fluid mechanics. Understand the issue of similarity in modeling situations of practical interest.

Learn and know how to apply knowledge that allows you to deal with the effects of roughness and boundary layer separations. Knowing how to apply appropriate theoretical tools to different regimes (laminar, turbulent) or flow regions. In this sense, knowing the fundamentals of turbulence and: knowing how to determine and using integral boundary layer parameters; achieve dexterity in manipulating the differential equations that govern the flows to reach results that allow analyzing them; know the effects of the longitudinal pressure gradient on the development of boundary layers; knowing how to use pressure coefficients for bodies immersed in flows, understanding and respecting ranges of applicability.

Learning and knowing how to apply the fundamentals of the study of flows where the effects of compressibility cannot be neglected. Know the phenomenon of choking, the operation of convergent-divergent nozzles, and shock waves, and know how to perform calculations in this context, also using tabulated information. Knowing how to solve fluid mechanics problems in the areas mentioned above, within the broad scope of Engineering and, in particular, mechanical engineering.

Develop skills in: information processing, autonomous work and self-learning, problem solving at engineering level, application of knowledge to new situations.

General characterization





Responsible teacher

Jorge Emanuel Pereira Navalho, Luís Miguel Chagas da Costa Gil


Weekly - 4

Total - 64

Teaching language



The program assumes mastery of the subjects covered in the Fluid Mechanics curricular unit.


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 presentaion of the syllabus of the curricular unit is done in theoretical-practical classes. After exposing the theoretical concepts, the professor proposes to the students the resolution and subsequent discussion of practical application problems. In addition to the theoretical-practical classes, students (organized into groups) carry out laboratory work.

Evaluation method

General Informations

  • The assessment in this curricular unit takes into account the following:
    • 1 laboratorial work
    • 2 tests or a final exam (written evaluation)
  • The final mark calculation (FM) is given by one of the following weighted averages which involve the mark of Test 1 (MT1), mark of Test 2 (MT2), the mark of the final Exam (MFE) and the mark of the laboratory work (MLW) — the values are rounded to one decimal place:

FM=0.45MT1+0.4MT2+0.15MLW      (1)

FM=0.85MFE+0.15MLW             (2)

If the student choose the final exam his final mark is calculated with Equation (2) — independetly of the value FM calculated with Equation (1).

  • To be approved at this curricular unit the student must verify the following criteria:
    • attend and deliver the report related to the laboratory work which should have a mark ≥ 8,0 val.; and 
    • obtain a final mark (NF) ≥ 9,5 val.
  • Final marks higher or equal to 17 val. can be subjected to an oral examination

Aditional informations and general rules for written evaluations

  • Written evaluation (tests and exams) are closed book. Any formulae, chart, or table required will be provided at the evaluation statement.
  • During the evaluation it is strictly forbidden the utilization of: (1) calculators with text storage capacity; (2) smartphones; (3) smartwatches; (4) any mean or device that allows data storage; (5) any mean or device that allows communication with other person or resource inside or outside the room where the evaluation is conducted. Transgressions are subjected to the RAC.
  • Only pen-answered questions are accepted. 
  • Students should make use of a classic watch (watch without any data storage capacity) to control the available time.
  • Students must register for the tests and exams during the corresponding time frames.

Subject matter

The program of this curricular unit is compoed by five modules (topics), which are descrived as follows.

Module I: Dimensional analysis and similarity — Application of the Buckingham Pi Theorem to relevant fluid mechanics cases; similarity, modeling and limitations. 

Module II: Differential equations — differential equations for mass conservation, linear momentum, Euler''s equations for inviscid flows; Navier-Stokes equations for newtonian fluids and the physical significance of each featured terms.

Module III: Turbulence — universal features of turbulent flows; Reynolds decomposition; and modeling of turbulent flows.

Module IV: Boundary layer flows — Prandtl''s theory of boundary flows; simplified equations for  inviscid flow; viscous fluid flows: effect of the Reynolds number and body geometry (streamlined and blunt bodies), boundary layer separation; boundary layer development over a flat plate: von Kármán integral analysis; boundary layer differential equations; Blasius exact solution (laminar boundary layer conditions); separation: effect of the pressure gradient; Thwaites'' method; flow over imersed bodies.

Module V: Compressible flows — Mach number (Ma); thermodynamics revisions; isentropic and adiabatic flow; estagnation properties; Mach number related properties; effect of the cross section area variation; choking; normal shock wave; supersonic bidimensional flow: Mach cone, oblique shock wave, Prandtl-Meyer expansion waves.



Programs where the course is taught: