Aula Teórica 1

```Aula Te&oacute;rica 1
Ramiro Neves, 1397
ramiro.neves@ist.utl.pt
www.mohid.com
Teachers
• Ramiro Neves, ext. 1397, 917224732
• ramiro.neves@ist.utl.pt
• www.mohid.com
• Guillaume Riflet, (Visual Basic)
• guillaume.riflet@gmail.com
• Offices: Pavilh&atilde;o de Mec&acirc;nica I, 1&ordm; floor.
Where tro use Fluid Mechanics?
www.mohid.com
Boussinesq Model
Douro Estuary mouth. West
and SW Waves
.
Thessaloniki NATO ARW (19-24 April
Integrated Basin Modelling
1D Drainage network
Q   Q 2


t
x  A
 H

Q2n2 

gA


0

A2 Rh4 / 3 

 x
2D Overland flow
A.Rh2 / 3 H / x
Q
n
3D Porous Media
 h z 

  K ( h) 


t
 xi xi 
Dia mundial da &aacute;gua, Cascais, 2007
Precipitation
Variable in Time
&amp; Space
Integrated Basin Modeling
Flow Production
• 2 Different Soils
• Infiltration
• Overland Flow
Rain Intensity
Integrated Basin Modeling
Sediment
Transport
• 2 Catchments
• 1 Reservoir
Rain Intensity
Dia mundial da &aacute;gua, Cascais, 2007
Classical Problems
Reduction of air resistance
Flow in a artery and
around a leaf.
Baloon fish
Low mobility high toxicity.....
At&eacute; as Bact&eacute;rias conhecem a
import&acirc;ncia da Mec&acirc;nica dos Fluidos
Difficulties?
• The formalism....
Difficulties are apparent because:
• Fluid Mechanics requires a FEW physical
concepts.
• Mathematical operators are mostly
• This course is an excellent opportunity to
consolidate basic concepts of Engineering
Sciences.
Set of courses downstream MFA
•
•
•
•
•
•
•
•
Transfer&ecirc;ncia de Energia e Massa.
Hidr&aacute;ulica Ambiental,
Hidrologia Ambiental e Recursos H&iacute;dricos,
F&iacute;sica da Atmosfera e do Oceano,
Ecologia....
Modela&ccedil;&atilde;o Ambiental,
Planeamento Biof&iacute;sico,
Requirements
• Physics: Forces, Newton law and acceleration,
kinetic energy, momentum, fluxes.
• Mathematics: derivative, integral, divergence,
products.
Conhecimentos a aquirir
• Compreens&atilde;o das equa&ccedil;&otilde;es da mec&acirc;nica dos
fluidos e dos processos que determinam o
movimento do fluido.
• Dom&iacute;nio dos conceitos de advec&ccedil;&atilde;o e de
difus&atilde;o e do conceito de equa&ccedil;&atilde;o de evolu&ccedil;&atilde;o
essenciais para as disciplinas a jusante.
MFA practical part
• A computational component is added to the classical
exercises with 3 objectives:
1. To show that Fluid Mechanics goes much beyond simple
analytical solutions;
2. To help students to enhance their programing skills.
3. 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...).
Bibliography
• Fluid Mechanics, Frank White, McGraw-Hill,
(or any other Fluid Mechanics Introduction
book de introdu&ccedil;&atilde;o).
• Apontamentos de Mec&acirc;nica dos Fluidos I
(Mec&acirc;nica).
• Lectures’ PPT.
Students Knowledge Assessment
• Tests/Exam (3/4),
• The Report on the computational exercise
(1/4).
What is a fluid?
• Is formed by molecules...
– That move, as in any other type of matter above 0 ̊K.
– 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).
Why is Fluid Mechanics distinct from
Solid Mechanics?
• 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 in
rest. Tangential shear moves the fluid in layers creating
Shear is proportional to
the rate of deformation.
Continuum Hypothesis
• 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?
What is the velocity?
• Velocity is the flux of volume per unit of area.
• The Velocity is defined in a point and thus is the flow per unit of
area, when the area tends to zero.
dQ
un 
dA
• 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 n one can write :

dQ
dQ
un 

 u .n 
dA
dA
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 definided in a point) we can compute the
discharge integrating the velocity along the whole area:


dVol
 dQ  u.n dA  Q   u.n dA  Q   u j n j dA
dt
A
A
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 na
elementary surface is:
And the flux of M across
a surface is:
dM
c
dVol

dM
dM dVol

 cdQ  cu.n dA
dt
dVol dt

m   cu.n dA
dm 
A
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….
```