Fluid Dynamics II


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, on the loss of load on ducts and accessories, in particular how to use the Moody diagram and obtain a pipe-system operation curve.
Know the fundamentals of the operation of pumps and fans, in order to select equipments to properly run in a facility.
Have knowledge of theoretical tools and their application to different flow regimes (laminar, turbulent) or regions of the flows. In this sense: 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

Daniel Cardoso Vaz, José Fernando de Almeida Dias


Weekly - 5

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.

Teaching method

There are theorectical and problem-solving classes, as well as a laboratory session.

In the theorectical classes the study matter is presented while giving space for questions by the students.

In the problem-solving sessions, the approach is centrered in the application of concepts, by proposing problems and practical cases and seeking the active participation of the students in solving them.

The laboratory session involves the registration of results of a wind tunnel test and the preparation of a report, twenty minutes within the end of the group''''''''s experimental session.

Evaluation method

1 - Assessment mode: continuous, through 3 elements: laboratory session and two written tests (theoretical-practical component) .

2 - Final grade

2.1. The weigh of the laboratorial component to the final grade is 15%, in accordance with no. 5 of art. 5 of the «Regulamento de Avaliação de Conhecimentos» (RAC), with the remaining 85% coming from the tests or exam. The first test weighs 45% while the second weighs 40%. 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.

2.2. If a students''''''''s final grade is equal or greater than 18 val., an oral exam may be scheduled for "grade defense".

3 - There is "qualification" (frequência), which is obtained by approval of the Laboratory Session, i.e., achievement of a grade equal or greater than 9.5 val..

4 - Laboratory Session

4.1. By Laboratory Session it is understood: attendance of the experimental trial, evidence of having prepared it, preparation and submission of a report (following a template) within the half-hour after the experimental trial.

4.2. For the Laboratory Session, the students should organise in groups of 3 and register until the deadline already announced in CLIP, in one of the sessions in a map to be divulged. The regent may intervene in the group formation in order to eliminate as much as possible the number of groups with 2 students.

4.3. The laboratory sessions take place in the working days between march 31st and april 8th, inclusive. There shall be none ad-hoc session atfer the 15th of abril (except in cases of  force majeure dully justified, that prevented the attendance in the nominal period), with due consequences in terms of lost of "qualification". 

4.4. The procedure for any situation not detailed here shall be determined by the regent.

5 - In 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. Buckingham''''''''s Π theorem. Physical interpretation of the nondimensional groups more common in fluid dynamics. Flow regimes (laminar, turbulent). Similitude, modelling and pitfalls.

Ducted flows. Distinction between internal and external flows. Energy conservation equation: generalized Bernoulli equation. Friction factor. Development of a ducted flow: entry region, laminar and turbulent flow, fully developed flow. Rugosity effect on head loss in ducts. Major losses. Characteristic curve of a pipe system. Ducts arranged in series and in parallel.

Pumps and fans. Basic operation-concepts. Classification. Curves of total head, power and efficiency. Pre-selection of pumps and fans. Operating point. Stability. Type of curve vs. application. Arrangement of pumps in series and in parallel. Cavitation and NPSH of a pump.

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.

5 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.


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