Fluid Mechanic

Code:

EBE0011

Acronym:

MFLU

Keywords
Classification	Keyword
OFICIAL	Engineering Sciences

Instance: 2020/2021 - 1S

Active?	Yes
Responsible unit:	Department of Chemical Engineering
Course/CS Responsible:	Master in Bioengineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIB	77	Syllabus	2	-	6	56	162

Teaching language

Portuguese

Objectives

It is expected that students develop a creative and critical thinking in the resolution of fluid mechanics problems, with particular emphasis on Bioengineering applications.

Learning outcomes and competences

Upon completing this course the student should be able to:
- Analyse and quantify the forces exerted by fluids on objects, either under static conditions (hydrostatics), or under flow conditions;
- Project fluid transport systems

Work in group and laboratory work competences will also be developed.

Working method

B-learning

Program

1. Introduction and fundamental concepts
Fluids, Fluid Mechanics and Bioengineering; Forces acting on a fluid element; Continuum and its limitations in biological systems; Newton’s law of viscosity; Dimensional homogeneity; Dimensions and unit systems; Newtonian and non-Newtonian fluids

2. Hydrostatics
Pressure on a fluid element; Absolute and relative pressure; Hydrostatic Fundamental Equation; Manometry; Hydrostatic paradox; Forces on immersed surfaces; Impulsion; Relative equilibrium; Applications

3. Fluid Kinematics
Eulerian and Langrangian description of a flow; Velocity and pressure fields; flow visualization; Velocity and acceleration vectors along a streamline

4. Bernoulli equation
Bernoulli equation along a streamline; Applications: free jets, flow meters (Venturi meter, orifice meter and weirs) and velocity meters (Pitot’s tube – examples in nature)

5. Dimensional analysis
Buckingham pi theorem; Common dimensionless groups in Fluid Mechanics; Theory of models; kinematic, dynamic and geometric similarity. Applications 

6. Finite control volume analysis
Continuity equation; Energy equation; Linear equation of motion; Applications

7. Laminar and turbulent flows
Laminar flow; Hagen-Poiseuille equation; Interior flows in organisms; Efficient bifurcation in blood vessels; Murray’s law. Turbulent flow: Reynolds’ experiment; fundamental concepts; velocity profile 

8. Flow in pipes and pumping systems
Head loss in pipes; Moody diagram; Local head loss; Equivalent length; Head loss in non-circular pipes; Equivalent diameter; Flow in multiple pipes; Pumping systems; Pumping dimensioning; Calculation of pumping power; characteristic curve and installation curve; Operating point; Applications 

9. Flow past immersed bodies
Qualitative interpretation and simple mathematical characterization; Pipe entry length; Boundary layer development; Drag and lift forces; Terminal velocity; Applications 

10. Non-Newtonian fluids (Basics)
Constitutive equations; Newtonian fluid model; Viscoelastic fluids; Elementary concepts of rheometry; Material functions; Blood rheology.

 

Additionally, the following laboratory works will be done:

- Flow rate measurement techniques

- Pump characteristic curves

- Laminar flow in a long tube

Mandatory literature

Bruce R. Munson... [et al.]; Fundamentals of fluid mechanics. ISBN: 978-0-470-39881-4
J.M. Campos; Notas para o Estudo da Mecânica de Fluidos, FEUP Edições, 2013

Teaching methods and learning activities

The theoretical concepts will be presented during theoretical-practical classes (twice a week, 1.5 h each), where some examples of application (and demonstrations) will be presented and discussed.

 

In the lab classes some experiments related with the course content will be done.

Students are advised to solve problems at home and the professor will be available to clarify students’ doubts.

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	37,50
Participação presencial	0,00
Teste	37,50
Trabalho laboratorial	25,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Apresentação/discussão de um trabalho científico	6,00
Elaboração de relatório/dissertação/tese	9,00
Estudo autónomo	80,00
Frequência das aulas	39,00
Trabalho laboratorial	26,00
Total:	160,00

Eligibility for exams

Attendance to classes, in accordance with the regulations of FEUP.

Calculation formula of final grade

The evaluation of this course can be done in two tests or in a final exam, and also includes a laboratory component:

Test 1 - To take place on November (date to be announced in advance).

Test 2 - Test about the program not covered by Test 1, to be done by students who have a mark equal or above 8 (in 20) in Test 1. Test 2 will take place at the same date and location of the final exam (normal season).

The final mark (CF) is calculated by:

CF = 0,25 x LAB + 0,75 x (NT1 + NT2)/2

where:
- LAB represents the mark in the lab component related with Fluid Mechanics (range 0-20)
- NT1 and NT2 are the marks on Tests 1 and 2, respectively (range 0-20). NT1 and NT2 need to be above 8 (range 0-20). 

If the classification obtained in Test 1 is less than 8 (in 20), instead of Test 2 the student will do a final exam (at the regular season), which will cover all the topics taught. In this case the final mark will be calculated from the lab component (LAB) and the mark obtained in the exam (EX): CF = 0,25 x LAB + 0,75 x EX.

Students with marks obtained in Test 1 above 8 (in 20) are given the option to do the final exam instead of the normal Test 2, covering all the topics taught in the discipline. In this case the final mark will be calculated as: CF = 0,25 x LAB + 0,75 x EX.

The exam of the special season covers the full program taught on the discipline, but the lab component is still included with 25% weight in the calculation of the final mark.

 

Students with approval in the laboratory component in previous years do not need to repeat this component, keeping the classification in the lab component (LAB) .

Special assessment (TE, DA, ...)

Final exam. The lab component is still included with 25% weight in the calculation of the final mark.

Classification improvement

Final exam. The lab component is still included with 25% weight in the calculation of the final mark.

Observations

n.a.