Aula Teórica 1&2

1. Aula Teórica 1&2 Ramiro Neves, 1397 ramiro.neves@ist.utl.pt www.mohid.com

2. Teachers • Ramiro Neves, ext. 1397, 917224732 • ramiro.neves@ist.utl.pt • www.mohid.com • David Brito, (Visual Basic) • guillaume.riflet@gmail.com • Offices: Pavilhão de MecânicaI, 1º floor.

3. Where to use FluidMechanics? • AboutEverywhere.....

4. www.mohid.com

5. BoussinesqModel . Douro Estuarymouth. West and SW Waves Thessaloniki NATO ARW (19-24 April 2005)

6. Integrated Basin Modelling 1D Drainage network 2D Overland flow Precipitation Variable in Time & Space 3D Porous Media Dia mundial da água, Cascais, 2007

7. Integrated Basin Modeling • Flow Production • 2 Different Soils • Infiltration • Overland Flow Rain Intensity

8. Integrated Basin Modeling • Sediment Transport • 2 Catchments • 1 Reservoir Rain Intensity Dia mundial da água, Cascais, 2007

9. ClassicalProblems

10. Reductionofairresistance

11. Flow in a artery and around a leaf.

12. Baloonfish Lowmobilityhightoxicity.....

13. Até as Bactérias conhecem a importância da Mecânica dos Fluidos

14. Difficulties? • Theformalism....

15. Difficulties are apparent because: • Fluid Mechanics requires a FEW physical concepts. • Mathematical operators are mostly derivatives, gradients and divergences. • This course is an excellent opportunity to consolidate basic concepts of Engineering Sciences.

16. Set of courses downstream MFA • Transferência de Energia e Massa. • Hidráulica Ambiental, • Hidrologia Ambiental e Recursos Hídricos, • Física da Atmosfera e do Oceano, • Ecologia.... • Modelação Ambiental, • Planeamento Biofísico, • Gestão Integrada de Bacias Hidrográficas.

17. Requirements • Physics: Forces, Newton law and acceleration, kinetic energy, momentum, fluxes. • Mathematics: derivative, integral, divergence, gradient, vector internal and external products.

18. Conhecimentos a aquirir • Compreensão das equações da mecânica dos fluidos e dos processos que determinam o movimento do fluido. • Domínio dos conceitos de advecção e de difusão e do conceito de equação de evolução essenciais para as disciplinas a jusante.

19. MFA practical part • A computational component is added to the classical exercises with 3 objectives: • To show that Fluid Mechanics goes much beyond simple analytical solutions; • To help students to enhance their programing skills. • To replace the classical laboratory lectures (laboratories were essential before computational methods were available). • This component will be consolidated with a group home work programmed using – preferentially - VBA. It is part of the MS Office is object oriented and useful for a wide range of engineering issues (database, internet...).

20. Bibliography • FluidMechanics, Frank White, McGraw-Hill, (oranyotherFluidMechanicsIntroductionbook de introdução). • Apontamentos de Mecânica dos Fluidos I (Mecânica). • Texts about specific subjects, • Lectures’ PPT.

21. StudentsKnowledgeAssessment • Tests/Exam (50%), • Mini Tests (25%) • Reporton the computationalexercise (25%)

22. Whatis a fluid? • Is formed by molecules... • That move, as in any other type of matter, above 0 kelvin. • The difference between a fluid and a solid is that in the fluid the molecules can change their relative positions allowing them to get the shape of the containers. • Fluids can be liquids or gases • In gases molecules have free relative movement. • In liquids molecules form groups with relative free movement (allowing them to get the shape of the container) which dimension depends on temperature (influencing their viscosity).

23. WhyisFluidMechanicsdistinctfromSolidMechanics? • In a fluid each molecule (or group of molecules) have relative movement freedom and not in solids. The consequence is that tangential stress deforms the fluids. Or in other words, if there is tangential stress there is movement. • Normal stress compress the fluid, that can remain at rest. Tangential shear moves the fluid in layers creating velocity gradients. Shearisproportional to the rate ofdeformation.

24. Elemental Volume • Is large enough to mantain the number of molecules, althoug they move and small enough to have uniform properties.

25. Continuum Hypothesis • The elemental volume is much larger than 10 nm • Necessary because we cannot assess the movement of individual molecules (too many and the Heisenberg principle) . • But they move individually.... • The unknown molecule movement will be dealt as diffusion in the equations. • When do we have velocity in a fluid? • When there is net mass transport across a surface. • What is velocity?

26. What is the velocity? • Velocity is the flux of volume per unit of area. • The Velocity is defined at a point and thus is the flow per unit of area, when the area tends to zero. • A surface can have 3 orientations in a tridimensional space and thus velocity can have up to 3 components. • The velocity component in one direction is the internal product of the velocity vector by the unitary vector along that direction. Using the surface normal one can write :

27. Discharge/ Advective Flux Knowing the 3 Velocity components and knowing that the velocity is the discharge per unit of area when the area tends to zero ( The velocity is defined in a point) we can compute the discharge integrating the velocity along the whole area: Defining a specific property as its value per unit of volume, (when the volume tends to zero) We can say that the flux of M across an elementary surface is: And the flux of M across a surface is:

28. Summary • We know what is fluid Mechanics and what for. • We know what is a fluid, • We know what is velocity and the advective flux. • We know that Fluid Mechanics aims to study flows and thus to know the velocity distributions. • To compute fluxes we also need to know specific properties distributions….